
Arrigo BONISOLI
Professore Ordinario Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede exMatematica

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2019
 A family of multigraphs with large palette index
[Articolo su rivista]
Avesani, M.; Bonisoli, A.; Mazzuoccolo, G.
abstract
Given a proper edgecoloring 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 edgecolorings of the multigraph itself. In this framework, the palette pseudograph of an edgecolored 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 2factors 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 2factor whose connected components are cycles of even length (an even 2factor). 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 edgeset of L(G) can be partitioned into three 2regular subgraphs whose connected components are cycles of even length. The more general problem of the existence of even cycle decompositions of index m in 2dregular 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 edgecoloring 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 edgecolorings of G. After reviewing some results on the palette index of regular graphs, we consider the problem of determining the palette index for nonregular 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 balancedtype spectra in graphdesigns
[Articolo su rivista]
Bonisoli, Arrigo; Ruini, Beatrice
abstract
For a given graph G, the set of positive integers v for which a Gdesign 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 Gdesigns 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 Gdesigns, degreebalanced and partially degreebalanced Gdesigns, orbitbalanced Gdesigns. We also address the existence question for nonbalanced Gdesigns, for Gdesigns which are either balanced or partially degreebalanced but not degreebalanced, for Gdesigns which are degreebalanced but not orbitbalanced.
2014
 On the existence spectrum for sharply transitive Gdesigns, 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 noncyclic 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 graphdesigns
[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 nonregular 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 degreebalanced Gdesigns. General properties of degreebalanced Gdesigns are studied and the spectrum of degreebalanced Gdesigns 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 degreebalanced.
2013
 Treedesigns with balancedtype conditions
[Articolo su rivista]
Bonisoli, Arrigo; Ruini, Beatrice
abstract
For a given graph G we say that a Gdesign 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 Gdesign is degreebalanced 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 vertexorbits of G under its automorphism group. A Gdesign is said to be orbitbalanced (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 Gdesign 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 Gdesign with v points exists, the values of v for which a degreebalanced Gdesign with v points exists, and the values of v for which an orbitbalanced Gdesign with v points exists.We also consider the existence problem for Gdesigns which are not balanced, which are balanced but not degreebalanced, and which are degreebalanced but not orbitbalanced.
2012
 Geometry, combinatorial designs and cryptology. Journal: Designs, Codes and Cryptography, vol. 64, n. 12 (July 2012), pp. 1227
[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 publickey cryptography to matters related to key distribution and authentication, from problems in graph theory to resolvability issues in designs, from finite projective planes to higherdimensional 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 “starterlike” methods. Existence may be a nontrivial 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 onefactorizations and the geometry of mixed translations
[Articolo su rivista]
Bonisoli, Arrigo; Bonvicini, Simona
abstract
We construct an infinite family of onefactorizations 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 onefactorizations which are live, in the sense that every onefactor 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 Gdecomposition 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 Gdecompositions 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 2factorizations
[Articolo su rivista]
Bonisoli, Arrigo; M., Buratti; Mazzuoccolo, Giuseppe
abstract
Let be a 2factorization of the complete graph Kv admitting an automorphism group G acting doubly transitively on the set of vertices. The vertexset V(Kv) can then be identified with the pointset of AG(n, p) and each 2factor of is the union of pcycles 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 of1factors 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 NPhard. 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 rgraphs.
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 Ginvariant 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 twotransitive 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 2transitively 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 noncyclic 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 nonexistence of a projective plane of order 15 with an A_4invariant 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 unitalderived (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 nonDesarguesian 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^41)/(q1). It can also be partitioned into 3dimensional 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 2subgroup S_2 and G has a normal subgroup M of odd order such that a G/M has a minimal normal 3subgroup. If the subgroup S generated by all involutory elations in G is nontrivial 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) 3group and n is congruent to 1 mod 3. In the latter case there exists a Ginvariant 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 socalled Hering's minimal subplane of P with respect to G.
2002
 Onefactorizations of complete graphs with vertexregular automorphism groups
[Articolo su rivista]
Bonisoli, Arrigo; Labbate, D.
abstract
We consider onefactorizations of K_2n possessing an automorphism group acting regularly (sharply transitively)on vertices. We present some upper bounds on the number of onefactors 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 nonexistence statements in case the number of fixed onefactors is as large as possible. Constructions both for dihedral groups and for some classes of abelian groups are given.
2000
 Each invertible sharply dtransitive finite permutation set with d >= 4 is a group
[Articolo su rivista]
Bonisoli, Arrigo; P., Quattrocchi
abstract
All known finite sharply 4transitive 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 4transitive 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 blocksymmetry is an automorphism. The above result has the following consequences, i) A sharply 5transitive permutation set on 12 elements containing the identity is necessarily the Mathieu group of degree 12. ii) There exists no sharply 6transitive permutation set on 13 elements. For d greater than or equal to 6 there exists no invertible sharply dtransitive permutation set on a finite set with at least d + 3 elements. iii) A finite invertible sharply dtransitive 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(2n1,q) suitably constructed from a Singer cycle of GL(n,q), we prove the existence of a partition of PG(2n1,q) consisting of two (n1)subspaces and caps, all having size (q^n1)/(q1) or (q^n1)/(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 nontrivial 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 TwoTransitive 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 2transitively 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 1dimensional 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 nonsolvable 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, onefactorizations 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 2transitively 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 onepointstabilizer of Sz(q) as an automorphism group and having q1 prescribed onefactors.
1995
 On twotransitive 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 2transitive if the plane admits a collineation group G ﬁxing Ω and acting 2transitively 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 2transitively on Ω then either n ∈ {2, 4} or n ≡ 0 mod 8 and the Sylow 2subgroups of G are generalized quaternion groups.The result is obtained by examining the action of G on a Ginvariant 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
 Pointprimitive 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 2transitive on the points of I unless n=3 and A_5 <= G <= A_5 * C_2
1992
 A property of sharply 3transitive finite permutation sets
[Relazione in Atti di Convegno]
Bonisoli, Arrigo; G., Korchmaros
abstract
Let G be a sharply 3transitive permutation set on PG(1,p^m), p odd, p^m > 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 2transitive 3nets
[Articolo su rivista]
Bonisoli, Arrigo
abstract
A 3net is said to be 2transitive if it admits a group of directionpreserving automorphisms fixing one of the transversal lines and acting 2transitively on its points. We classify the 2transitive finite 3nets which do not admit a proper 2transitive 3subnet, except, possibly for a subnet of order 2. The result is then extended under a weaker assumption.
1990
 A Characterization of the sharply 3transitive finite permutation groups
[Articolo su rivista]
Bonisoli, Arrigo; Korchmaros, G.
abstract
Generalizing a result by N. Percsy, we prove a sufficient conditionfor a sharply 3transitive 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
 MDSCodes, nets and column orthogonal latin rectangles
[Articolo su rivista]
Bonisoli, Arrigo; Fiori, Carla
abstract
1988
 Sharply 1transitive subsets of certain permutation groups
[Articolo su rivista]
Bonisoli, A.; Fiori, Carla
abstract
We give a method for constructing sharply 1transitive permutation sets inside a finite permutation group with certain properties and we apply this method to obtain a family of sharply 1transitive permutation subsets of the sharply 3transitive 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.