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A semilinear space S is a non-empty set of elements called points, provided with a collection of subsets called lines such that any pair of points is contained in at most one line and every line contains at least two points. Two points p and q are said to be collinear if p T q and if the pair f p; qg is contained in a line; the line containing two… (More)
A partial linear space is a non-empty set of points, provided with a collection of subsets called lines such that any pair of points is contained in at most one line and every line contains at least two points. Graphs and linear spaces are particular cases of partial linear spaces. A partial linear space which is neither a graph nor a linear space is called… (More)
A transitive decomposition of a graph is a partition of the edge set together with a group of automorphisms which transitively permutes the parts. In this paper we determine all transitive decompositions of the Johnson graphs such that the group preserving the partition is arc-transitive and acts primitively on the parts.
An S 3-involution graph for a group G is a graph with vertex set a union of conjugacy classes of involutions of G such that two involutions are adjacent if they generate an S 3-subgroup in a particular set of conjugacy classes. We investigate such graphs in general and also for the case where G = PSL(2, q).
A Latin square design whose automorphism group is transitive of rank at most 3 on points must come from the multiplication table of an elementary abelian p-group, for some prime p.
A classification is given of rank 3 group actions which are quasiprim-itive but not primitive. There are two infinite families and a finite number of individual imprimitive examples. When combined with earlier work of Bannai, Kantor, Liebler, Liebeck and Saxl, this yields a classification of all quasiprimitive rank 3 permutation groups. Our classification… (More)
We prove that the complex of proper non-trivial non-degenerate subspaces of a finite-dimensional vector space endowed with a non-degenerate sesquilinear form is homo-topy equivalent to a wedge of spheres. Additionally, we show that the same is true for a slightly wider class of simplicial complexes, the so-called generalized Phan ge-ometries of type A n.… (More)