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Arrigo BONISOLI

Professore Ordinario
Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede ex-Matematica

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Pubblicazioni

2019 - A family of multigraphs with large palette index [Articolo su rivista]
Avesani, M.; Bonisoli, A.; Mazzuoccolo, G.
abstract

Given a proper edge-coloring of a loopless multigraph, the palette of a vertex is defined as the set of colors of the edges which are incident with it. The palette index of a multigraph is defined as the minimum number of distinct palettes occurring among the vertices, taken over all proper edge-colorings of the multigraph itself. In this framework, the palette pseudograph of an edge-colored multigraph is defined in this paper and some of its properties are investigated. We show that these properties can be applied in a natural way in order to produce the first known family of multigraphs whose palette index is expressed in terms of the maximum degree by a quadratic polynomial. We also attempt an analysis of our result in connection with some related questions.

2017 - Even cycles and even 2-factors in the line graph of a simple graph [Articolo su rivista]
Bonisoli, Arrigo; Bonvicini, Simona
abstract

Let G be a connected graph with an even number of edges. We show that if the subgraph of G induced by the vertices of odd degree has a perfect matching, then the line graph of G has a 2-factor whose connected components are cycles of even length (an even 2-factor). For a cubic graphG, we also give a necessary and sufficient condition so that the corresponding line graph L(G) has an even cycle decomposition of index 3, i.e., the edge-set of L(G) can be partitioned into three 2-regular subgraphs whose connected components are cycles of even length. The more general problem of the existence of even cycle decompositions of index m in 2d-regular graphs is also addressed.

2017 - On the palette index of a graph: the case of trees [Articolo su rivista]
Bonisoli, Arrigo; Bonvicini, Simona; Mazzuoccolo, Giuseppe
abstract

The palette of a vertex v of a graph G in a proper edge-coloring is the set of colors assigned to the edges which are incident with v. The palette index of G is the minimum number of palettes occurring among all proper edge-colorings of G. After reviewing some results on the palette index of regular graphs, we consider the problem of determining the palette index for non-regular graphs. We begin by considering the family of trees. We give an upper bound for the palette index of a tree in terms of the maximum degree Δ. We show that this bound is best possible by producing, for each Δ≥ 3, a tree T^ Δ whose palette index reaches the upper bound.

2015 - Balance, partial balance and balanced-type spectra in graph-designs [Articolo su rivista]
Bonisoli, Arrigo; Ruini, Beatrice
abstract

For a given graph G, the set of positive integers v for which a G-design exists is usually called the 'spectrum' for G and the determination of the spectrum is sometimes called the 'spectrum problem'. We consider the spectrum problem for G-designs satisfying additional conditions of 'balance', in the case where G is a member of one of the following infinite families of trees: caterpillars, stars, comets, lobsters and trees of diameter at most 5. We determine the existence spectrum for balanced G-designs, degree-balanced and partially degree-balanced G-designs, orbit-balanced G-designs. We also address the existence question for non-balanced G-designs, for G-designs which are either balanced or partially degree-balanced but not degree-balanced, for G-designs which are degree-balanced but not orbit-balanced.

2014 - On the existence spectrum for sharply transitive G-designs, G a [k]-matching [Articolo su rivista]
Bonisoli, Arrigo; Bonvicini, Simona
abstract

In this paper we consider decompositions of the complete graph Kv into matchings of uniform cardinality k. They can only exist when k is an admissible value, that is a divisor of v(v−1)/2 with 1≤k≤v/2. The decompositions are required to admit an automorphism group Γ acting sharply transitively on the set of vertices. Here Γ is assumed to be either non-cyclic abelian or dihedral and we obtain necessary conditions for the existence of the decomposition when k is an admissible value with 1<k<v/2. Differently from the case where Γ is a cyclic group, these conditions do exclude existence in specific cases. On the other hand we produce several constructions for a wide range of admissible values, in particular for every admissible value of k when v is odd and Γ is an arbitrary group of odd order possessing a subgroup of order gcd(k,v).

2013 - A hierarchy of balanced graph-designs [Articolo su rivista]
Bonisoli, Arrigo; Bonvicini, Simona; Rinaldi, Gloria
abstract

Decompositions of the complete graph K_v into subgraphs, all of which are isomorphic to some given non-regular graph G are considered. The decompositions are required to have the additional property that each vertex occurs a constant number of times as a vertex of given degree in the subgraphs of the decomposition. These decompositions are said to be degree-balanced G-designs. General properties of degree-balanced G-designs are studied and the spectrum of degree-balanced G-designs is determined when G is a bowtie. Moreover, for each v in this spectrum, there exists a bowtie design on v vertices which is not degree-balanced.

2013 - Tree-designs with balanced-type conditions [Articolo su rivista]
Bonisoli, Arrigo; Ruini, Beatrice
abstract

For a given graph G we say that a G-design is balanced if there exists a constant r such that for each point x the number of blocks containing x is equal to r. A G-design is degree-balanced if, for each degree d occurring in the graph G, there exists a constant r_d such that, for each point x, the number of blocks containing x as a vertex of degree d is equal to r_d.Let V_1, V_2, . . . , V_h be the vertex-orbits of G under its automorphism group. A G-design is said to be orbit-balanced (or strongly balanced) if for i = 1, 2, . . . , h there exists a constant R_i such that, for each point x the number of blocks of the G-design in which x occurs as an element in the orbit V_i is equal to R_i.If G is a tree with six vertices, we determine the values of v for which a balanced G-design with v points exists, the values of v for which a degree-balanced G-design with v points exists, and the values of v for which an orbit-balanced G-design with v points exists.We also consider the existence problem for G-designs which are not balanced, which are balanced but not degree-balanced, and which are degree-balanced but not orbit-balanced.

2012 - Geometry, combinatorial designs and cryptology. Journal: Designs, Codes and Cryptography, vol. 64, n. 1-2 (July 2012), pp. 1-227 [Direzione o Responsabilità Riviste]
Bonisoli, Arrigo; J., Hirschfeld; S., Magliveras; D., Jungnickel; J. D., Key; C. J., Mitchell
abstract

2012 - Preface: geometry, combinatorial designs and cryptology [Scheda bibliografica]
Bonisoli, Arrigo; J., Hirschfeld; S., Magliveras
abstract

This issue of the journal is devoted to the themes of Geometry, Combinatorial Designs and Cryptology. The guest editors (who are the authors of this preface) selected sixteen contributions covering various areas within these themes, ranging from public-key cryptography to matters related to key distribution and authentication, from problems in graph theory to resolvability issues in designs, from finite projective planes to higher-dimensional geometries.

2011 - Atti del Seminario Matematico e Fisico dell'Università di Modena e Reggio Emilia, vol. 58 [Direzione o Responsabilità Riviste]
Bonisoli, Arrigo
abstract

2010 - Atti del Seminario Matematico e Fisico dell'Università di Modena e Reggio Emilia [Direzione o Responsabilità Riviste]
Bonisoli, Arrigo
abstract

2010 - Discrete Mathematics: Preface [Articolo su rivista]
Bonisoli, A.; Ghinelli, D.; Gionfriddo, M.; Korchmros, G.; Lunardon, G.; Marchi, M.; Pellegrini, S.
abstract

2009 - Atti del Seminario Matematico e Fisico dell'Università di Moena e Reggio Emilia [Direzione o Responsabilità Riviste]
Bonisoli, Arrigo
abstract

2009 - Graph Decompositions and Symmetry [Capitolo/Saggio]
Bonisoli, Arrigo
abstract

In this paper I shall try to review some results which were obtained in the area of factorizations and decompositions of complete graphs admitting an automorphism group with some specified properties. These properties primarily involve the action of the group on the objects of the decomposition, most oftenvertices, but also edges, subgraphs of the decomposition or factors of the factorization.Classification theorems were obtained in highly symmetric situations, for example when the group acts doubly transitively on vertices, and it is often the case that all examples arise from geometry in this context.A “less” symmetric situation involves a group acting sharply transitively on vertices, which means for any two given vertices there exists precisely one group element mapping the first vertex to the second one. The vertices of the complete graph can be identified with group elements in this case, and the decompositionor factorization can be described entirely within the group by techniques which are generally known as “difference” or “starter-like” methods. Existence may be a non-trivial question and generally depends on the isomorphism type of the chosen group.

2009 - Parallelism [Articolo su rivista]
Bonisoli, Arrigo
abstract

Problems involving the idea of parallelism occur in finite geometry and in graph theory. This article addresses the question of constructing parallelisms with some degree of “symmetry”. In particular, can we say anything on parallelisms admitting an automorphism group acting doubly transitively on “parallel classes”?

2008 - Primitive one-factorizations and the geometry of mixed translations [Articolo su rivista]
Bonisoli, Arrigo; Bonvicini, Simona
abstract

We construct an infinite family of one-factorizations of K_v admitting an automorphism group acting primitively on the set ofvertices but no such group acting doubly transitively. We also give examples of one-factorizations which are live, in the sense that every one-factor induces an automorphism, but do not coincide with the affine line parallelism of AG(n, 2). To this purpose we develop the notion of a “mixed translation” in AG(n, 2).

2008 - Sharply transitive decompositions of complete graphs into generalized Petersen graphs [Articolo su rivista]
Bonisoli, Arrigo; M., Buratti; Rinaldi, Gloria
abstract

A decomposition of the complete graph K_v into copies of a subgraph G is called a sharply transitive G-decomposition if it is left invariant by an automorphism group acting sharply transitively on the vertex set of K_v. For suitable values of v we construct examples of sharply transitive G-decompositions when G is either a Petersen graph, a generalized Petersen graph or a prism.

2007 - Atti del Seminario Matematico e Fisico dell'Università di Modena e Reggio Emilia, vol. 55 [Direzione o Responsabilità Riviste]
Bonisoli, Arrigo
abstract

2007 - Doubly transitive 2-factorizations [Articolo su rivista]
Bonisoli, Arrigo; M., Buratti; Mazzuoccolo, Giuseppe
abstract

Let be a 2-factorization of the complete graph Kv admitting an automorphism group G acting doubly transitively on the set of vertices. The vertex-set V(Kv) can then be identified with the point-set of AG(n, p) and each 2-factor of is the union of p-cycles which are obtained from a parallel class of lines of AG(n, p) in a suitable manner, the group G being a subgroup of A G L(n, p) in this case. The proof relies on the classification of 2-(v, k, 1) designs admitting a doubly transitive automorphism group. The same conclusion holds even if G is only assumed to act doubly homogeneously.

2007 - Excessive Factorizations of Regular Graphs [Relazione in Atti di Convegno]
Bonisoli, Arrigo; D., Cariolaro
abstract

An excessive factorization of a graph G is a minimum set F of1-factors of G whose union is E(G). In this paper we study excessive factorizations of regular graphs. We introduce two graph parameters related to excessive factorizations and show that their computation is NP-hard. We pose a number of questions regarding these parameters. We show that the size of an excessive factorization of a regular graph can exceed the degree of the graph by an arbitrarily large quantity. We conclude with a conjecture on the excessive factorizations of r-graphs.

2007 - Irreducible collineation groups with two orbits forming an oval [Articolo su rivista]
A., Aguglia; Bonisoli, Arrigo; G., Korchmaros
abstract

Let G be a collineation group of a finite projective plane P of odd order fixing an oval Ω. We investigate the case in which G has even order, has two orbits Ω_0 and Ω_1 on Ω, and the action of G on Ω_0 is primitive.We show that if G is irreducible, then P has a G-invariant desarguesian subplane P_0 and Ω_0 is a conic of P_0.

2006 - Atti del Seminario Matematico e Fisico dell'Università di Modena e Reggio Emilia, vol. 54 [Direzione o Responsabilità Riviste]
Bonisoli, Arrigo
abstract

2005 - Atti del Seminario Matematico e Fisico dell'Università di Modena e Reggio Emilia, vol. 53, fasc. 1 [Direzione o Responsabilità Riviste]
Bonisoli, Arrigo
abstract

2005 - Atti del Seminario Matematico e Fisico dell'Università di Modena e Reggio Emilia, vol. 53, fasc. 2 [Direzione o Responsabilità Riviste]
Bonisoli, Arrigo
abstract

2005 - On two-transitive parabolic ovals [Articolo su rivista]
Bonisoli, Arrigo; Rinaldi, Gloria
abstract

The state of knowledge on the following problem is examined. Let P be a projective plane of odd order n with an oval S and let G be a collineation group of P fixing S. Assume G fixes a point Q on S and acts 2-transitively on S - {Q}. The usual basic question is: what can be said about the plane P, the oval S and the group G?

2005 - Quaternionic starters [Articolo su rivista]
Bonisoli, Arrigo; Rinaldi, Gloria
abstract

Let m be an integer, m >= 2 and set n = 2^m. Let G be a non-cyclic group of order 2n admitting a cyclic subgroup of order n. We prove that G always admits a starter. Therefore, there exists a one - factorization of the complete graph on 2n vertices admitting G as an automorphism group acting sharply transitively on the vertex set. For an arbitrary even n > 2 we also show the existence of a starter in the dicyclic group of order 2n.

2004 - Atti del Seminario Matematico e Fisico dell'Università di Modena e Reggio Emilia, vol. 52, fasc. 1. [Direzione o Responsabilità Riviste]
Bonisoli, Arrigo
abstract

2004 - Atti del Seminario Matematico e Fisico dell'Università di Modena e Reggio Emilia, vol. 52, fasc. 2. [Direzione o Responsabilità Riviste]
Bonisoli, Arrigo
abstract

2004 - On the non-existence of a projective plane of order 15 with an A_4-invariant oval [Articolo su rivista]
A., Aguglia; Bonisoli, Arrigo
abstract

Let P be a projective plane of order 15 with an oval O. Assume P admits a collineation group G fixing O such that G is isomorphic to A_4 and the action of G on O yields precisely two orbits O(1) and O(2) with |O(2)|= 4. We prove that the Buekenhout oval arising from O cannot exist.

2003 - A class of complete arcs in multiply derived planes [Articolo su rivista]
Bonisoli, Arrigo; Rinaldi, Gloria
abstract

We prove that unital-derived (q^2 - q + 1)-arcs of PG(2, q^2) still yield complete arcs after multiple derivation with respect to disjoint derivation sets on a given line.

2003 - Intransitive collineation groups of ovals fixing a triangle [Articolo su rivista]
A., Aguglia; Bonisoli, Arrigo
abstract

We investigate collineation groups of a finite projective plane of odd order fixing an oval and having two orbits on it, one of which is assumed to be primitive. The situation in which there exists a fixed triangle off the oval is considered in detail. Our main result is the following. Theorem. Let P be a finite projective plane of odd order n containing an oval O. If a collineation group G of P satisfies the properties: (a) G fixes O and the action of G on O yields precisely two orbits O_1 and O_2, (b) G has even order and a faithful primitive action on O_2, (c) G fixes neither points nor lines but fixes a triangle ABC in which the points A, B, C are not on the oval O, then n is an element of {7, 9, 27}, the orbit O_2 has length 4 and G acts naturally on O_2 as A_4 or S_4. Each order n in {7, 9, 27} does furnish at least one example for the above situation; the determination of the planes and the groups which do occur is complete for n = 7, 9; the determination of the planes is still incomplete for n = 27.

2003 - Primitive collineation groups of ovals with a fixed point [Articolo su rivista]
Bonisoli, Arrigo; Rinaldi, Gloria
abstract

We investigate collineation groups of a finite projective plane of odd order n fixing an oval and having two orbits on it, one of which is assumed to be primitive. The situation in which the group fixes a point off the oval is considered. We prove that it occurs in a Desarguesian plane if and only if (n + 1)/2 is an odd prime, the group lying in the normalizer of a Singer cycle of PGL(2, n) in this case. For an arbitrary plane we show that the group cannot contain Baer involutions and derive a number of structural and numerical properties in the case where the group has even order. The existence question for a non-Desarguesian example is addressed but remains unanswered, although such an example cannot have order n less than or equal to 23 as computer searches carried out with GAP show.

2002 - Cap partitions of the Segre Variety S_1,3 [Articolo su rivista]
R. D., Baker; Bonisoli, Arrigo; A., Cossidente; G. L., Ebert
abstract

We prove that the Segre variety S_1,3 of PG(7,q) can be partitioned into caps of size (q^4-1)/(q-1). It can also be partitioned into 3-dimensional elliptic quadrics or into twisted cubics.

2002 - Irreducible collineation groups fixing a hyperoval [Articolo su rivista]
Bonisoli, Arrigo; G., Korchmaros
abstract

Let G be an irreducible collineation group of a finite projective plane P of even order n congruent to 0 mod 4. Our goal is to determine the structure of G under the hypothesis that G fixes a hyperoval W of P. We assume |G| congruent to 0 mod 4. If G has no involutory elation, then G = O(G) x S_2 with a cyclic Sylow 2-subgroup S_2 and G has a normal subgroup M of odd order such that a G/M has a minimal normal 3-subgroup. If the subgroup S generated by all involutory elations in G is non-trivial and Z(S) denotes its center, then either S is isomrphic to Alt(6) and n = 4, or S/Z(S) is isomorphic to (C_3 x C_3) x C_2, Z(S) is a (possibly trivial) 3-group and n is congruent to 1 mod 3. In the latter case there exists a G-invariant subplane P_0 in P such that the collineation group G_0 induced by G on P_0 is irreducible and fixes a hyperoval W_0. Furthermore, the subgroup S_0 generated by all involutory elations in G_0 is a generalized Hessian group of order 18, that is S_0 is isomorphic to (C_3 x C_3) x C_2 and the configuration of the centers of the involutory elations in G_0 consists of the nine inflexions of an equianharmonic cubic of a subplane P_1 of order 4. In particular, P_1 is generated by the centers and the axes of all involutory elations in G, and hence it is the so-called Hering's minimal subplane of P with respect to G.

2002 - One-factorizations of complete graphs with vertex-regular automorphism groups [Articolo su rivista]
Bonisoli, Arrigo; Labbate, D.
abstract

We consider one-factorizations of K_2n possessing an automorphism group acting regularly (sharply transitively)on vertices. We present some upper bounds on the number of one-factors which are fixed by the group; further informationis obtained when equality holds in these bounds. The case where the group is dihedral is studied in some detail, with some non-existence statements in case the number of fixed one-factors is as large as possible. Constructions both for dihedral groups and for some classes of abelian groups are given.

2000 - Each invertible sharply d-transitive finite permutation set with d >= 4 is a group [Articolo su rivista]
Bonisoli, Arrigo; P., Quattrocchi
abstract

All known finite sharply 4-transitive permutation sets containing the identity are groups, namely S_4, S_5, A_6 and the Mathieu group of degree 11. We prove that a sharply 4-transitive permutation set on 11 elements containing the identity must necessarily be the Mathieu group of degree 11. The proof uses direct counting arguments. It is based on a combinatorial property of the involutions in the Mathieu group of degree 11 (which is established here) and on the uniqueness of the Minkowski planes of order 9 (which had been established before): the validity of both facts relies on computer calculations. A permutation set is said to be invertible if it contains the identity and if whenever it contains a permutation it also contains its inverse. In the geometric structure arising from an invertible permutation set at least one block-symmetry is an automorphism. The above result has the following consequences, i) A sharply 5-transitive permutation set on 12 elements containing the identity is necessarily the Mathieu group of degree 12. ii) There exists no sharply 6-transitive permutation set on 13 elements. For d greater than or equal to 6 there exists no invertible sharply d-transitive permutation set on a finite set with at least d + 3 elements. iii) A finite invertible sharply d-transitive permutation set with d greater than or equal to 4 is necessarily a group, that is either a symmetric group, an alternating group, the Mathieu group of degree 11 or the Mathieu group of degree 12.

2000 - Mixed Partitions of Projective Geometries [Articolo su rivista]
Bonisoli, Arrigo; A., Cossidente
abstract

Starting from a linear collineation of PG(2n-1,q) suitably constructed from a Singer cycle of GL(n,q), we prove the existence of a partition of PG(2n-1,q) consisting of two (n-1)-subspaces and caps, all having size (q^n-1)/(q-1) or (q^n-1)/(q+1) according as n is odd or even respectively. Similar partitions of quadrics or hermitian varieties into two maximal totally isotropic subspaces and caps of equal size are also obtained. We finally consider the possibility of partitioning the Segre variety S_2,2 of PG(8,q) into caps of size q^2+q+1 which are Veronese surfaces.

1999 - Irreducible Collineation Groups fixing an Oval [Articolo su rivista]
Bonisoli, Arrigo; M. R., Enea; G., Korchmaros
abstract

In this paper we consider an oval which is fixed by an irreduciblecollineation group whose order is divisible by four. Our main result, states that such a group contains non-trivial involutory perspectivities, hence a theorem of Hering describing such groups applies. The consequences of such a classification in the situation under consideration are analyzed in some detail.

1999 - Mixed Partitions of PG(5,q) [Articolo su rivista]
R. D., Baker; Bonisoli, Arrigo; A., Cossidente; G. L., Ebert
abstract

We prove that the projective space PG(5,q) can be partitioned into two planes and q^3−1 caps all of which are quadric Veroneseans. This partition is obtained by taking the orbits of alifted Singer cycle of PG(2,q). The possibility of getting larger caps by gluing some of these orbits together is also addressed.

1997 - On a Theorem of Hering and Two-Transitive Ovals with a Fixed External Line [Relazione in Atti di Convegno]
Bonisoli, Arrigo
abstract

Let O be an oval in a finite projective plane of even order n admitting a collineation group G acting 2-transitively on the points of the oval. If G fixes an external line then the group G is described in some detail and, using a result of Hering, is shown to contain the 1-dimensional affine semilinear group in its natural permutation representation.

1997 - Some Multiply Derived Translation Planes with SL(2,5) as an Inherited Collineation Group in the Translation Complement [Articolo su rivista]
Bonisoli, Arrigo; G., Korchmaros; T., Szonyi
abstract

Finite translation planes having a collineation group isomorphic to SL(2,5) occur in many investigations on minimal normal non-solvable subgroups of linear translation complements. In this paper, we are looking for multiply derived translation planes of the desarguesian plane which have an inherited linear collineation group isomorphic to SL(2,5). The Hall plane and some of the planes discovered by Prohaska are translation planes of this kind of order q^2, provided that q is odd and either q^2 is congruent 1 mod 5 or q is a power of 5. In this paper the case q congruent -1 mod 5 is considered and some examples are constructed under the further hypotesis that q is congruent 2 mod 3, or q is congruent 1 mod 3 and q is congruent 1 mod 4, or q is congruent -1 mod 4, 3 does not divide q and q is congruent 3, 5, or 6 mod 7. One might expect that examples exist for each odd prime power q. But this is not always true according to Theorem 2.

1996 - Partitioning projective geometries into Segre varieties [Articolo su rivista]
Bonisoli, Arrigo; A., Cossidente; D., Saeli
abstract

Using suitable subgroups of Singer cyclic groups we prove some properties of regular spreads and Segre varieties, which in turn yield a necessary and sufficient condition for partitioning a finite projective space into such varieties.

1996 - Suzuki groups, one-factorizations and Lueneburg planes. [Articolo su rivista]
Bonisoli, Arrigo; G., Korchmaros
abstract

In this paper we give a method for studying a plane of order q^2 admitting Sz(q) as a collineation group fixing an oval and acting 2-transitively on its points; we prove in particular that for q=8 the dual Lueneburg plane is the unique plane with this property. We also determine all one factorizations of the complete graph on q^2 vertices admitting the one-point-stabilizer of Sz(q) as an automorphism group and having q-1 prescribed one-factors.

1995 - On two-transitive ovals in projective planes of even order [Articolo su rivista]
Bonisoli, Arrigo; G., Korchmaros
abstract

An oval Ω in a finite projective plane is said to be 2-transitive if the plane admits a collineation group G fixing Ω and acting 2-transitively on its points. In the order n of the plane is assumed to be even then the following result is proved.Theorem. If G fixes an external line and acts 2-transitively on Ω then either n ∈ {2, 4} or n ≡ 0 mod 8 and the Sylow 2-subgroups of G are generalized quaternion groups.The result is obtained by examining the action of G on a G-invariant family of pairwise disjoint ovals (including Ω) with a common knot.

1994 - Incidence structures and permutation sets [Articolo su rivista]
Bonisoli, Arrigo; P., Quattrocchi
abstract

Some relations between permutation sets and certain incidence structures (in particular: Minkowski planes) are illustrated and surveyed. In connection with the existence problem for flocks in arbitrary (B)-geometries yielding translation planes, a construction for sharply transitive subsets of the semilinear groups PGammaL(n,q) is given.

1993 - Point-primitive inversive planes of odd order [Articolo su rivista]
Bonisoli, Arrigo
abstract

The following Theorem is proved. If I is a finite inversive plane of odd order n and G is an automorphism group of I acting primitively on its points, then I is miquelian; furthermore, we have PSL(2,n^2) <= G <= PGammaL(2,n^2) and G is 2-transitive on the points of I unless n=3 and A_5 <= G <= A_5 * C_2

1992 - A property of sharply 3-transitive finite permutation sets [Relazione in Atti di Convegno]
Bonisoli, Arrigo; G., Korchmaros
abstract

Let G be a sharply 3-transitive permutation set on PG(1,p^m), p odd, p^m &gt; 9. Suppose G contains all the involutions in PGL(2,p^m) and is such that if a permutation g lies in G then so does every power of g. We have that G necessarily coincides with PGL(2, p^m)

1992 - Flocks of hyperbolic quadrics and linear groups containing homologies [Articolo su rivista]
Bonisoli, Arrigo; G., Korchmaros
abstract

The classification of the subgroups of PGL(2,q) can be used to obtain the classification of the flocks of the hyperbolic quadrics in PG(3,q). A description of the group of all linear collineations preserving a given flock is also obtained.

1992 - Sulla famiglia dei flocks lineari di una quadrica iperbolica assolutamente irriducibile di uno spazio proiettivo finito [Articolo su rivista]
Bonisoli, Arrigo; G., Faina
abstract

On the family of linear flocks of an absolutely irreducible quadric in a finite projective space. In this Note we give a characterization of the set of all linear flocks of the absolutely irreducible hyperbolic quadric in PG(3,q).

1991 - On 2-transitive 3-nets [Articolo su rivista]
Bonisoli, Arrigo
abstract

A 3-net is said to be 2-transitive if it admits a group of direction-preserving automorphisms fixing one of the transversal lines and acting 2-transitively on its points. We classify the 2-transitive finite 3-nets which do not admit a proper 2-transitive 3-subnet, except, possibly for a subnet of order 2. The result is then extended under a weaker assumption.

1990 - A Characterization of the sharply 3-transitive finite permutation groups [Articolo su rivista]
Bonisoli, Arrigo; Korchmaros, G.
abstract

Generalizing a result by N. Percsy, we prove a sufficient conditionfor a sharply 3-transitive finite permutation set with identity to be a group; the proof makes use of M. J. Kallaher's theorem on finite Bol quasifields

1990 - Finite Translation Planes Arising from ASL(1,9)-Invariant Spreads [Articolo su rivista]
Bonisoli, Arrigo; D., Defina; D., Saeli
abstract

In this work we study spreads of PG(3,q) which are invariant under the group ASL(1,9) of affine special linear transformations over GF(9); such group is contained in A_6 as a subgroup of index 10. Under the assumption q odd, q congruent 1 (mod 3) we give a convenient representation of ASL(1,9) inside PGL(4,q) and moreover we settle the case q=7 completely.

1990 - MDS-Codes, nets and column orthogonal latin rectangles [Articolo su rivista]
Bonisoli, Arrigo; Fiori, Carla
abstract

1988 - Sharply 1-transitive subsets of certain permutation groups [Articolo su rivista]
Bonisoli, A.; Fiori, Carla
abstract

We give a method for constructing sharply 1-transitive permutation sets inside a finite permutation group with certain properties and we apply this method to obtain a family of sharply 1-transitive permutation subsets of the sharply 3-transitive permutation group M(p^2f) for p^f = 1 (mod4)

1984 - Every equidistant linear code is a sequence of dual Hamming codes [Articolo su rivista]
Bonisoli, Arrigo
abstract

If an equidistant linear code exists, then its parameters must satisfy certain relations determined by the Plotkin bound. For each set of possible parameters there actually exists an equidistant linear code with these parameters: its generator matrix is a sequence of parity check matrices of Hamming codes. The generator matrix of every equidistant linear code can be brought to this form by suitably rearranging its columns.