We give a characterization of the ‘special linear groups’ T (Ψ,W ) as linear groups generated by a non-degenerate class Σ of abstract root groups such that the elements of A ∈ Σ are transvections.

‎There are a few finite groups that are determined up to isomorphism solely by their order, such as $mathbb{Z}_{2}$ or $mathbb{Z}_{15}$. Still other finite groups are determined by their order together with other data, such as the number of elements of each order, the structure of the prime graph, the number of order components, the number of Sylow $p$-subgroups for each prime $p$, etc. In this...

In this article we look into characterizing primitive groups in the following way. Given a primitive group we single out a subset of its generators such that these generators alone (the so-called primitive generators) imply the group is primitive. The remaining generators ensure transitivity or comply with specific features of the group. We show that, other than the symmetric and alternating gr...

This article is a contribution to the study of the automorphism groups of 2 − (v, k, 1) designs. Let G act as a block-transitive and point-primitive automorphism group of a non-trivial design D with v points and blocks of size k. Set k2 = (k, v−1). Assume q = pf for some prime p and positive integer f . If q ≥ [(k2k − k2 + 1)f ]2, then Soc(G), the socle of G, is not PSL(2, q). Mathematics Subje...

In recent years the term ‘chiral’ has been used for geometric and combinatorial figures which are symmetrical by rotation but not by reflection. The correspondence of groups and polytopes is used to construct infinite series of chiral and regular polytopes whose facets or vertex-figures are chiral or regular toroidal maps. In particular, the groups PSL,(Z,) are used to construct chiral polytope...