Factorisations of characteristically simple groups

C-Characteristically Simple Groups

Let G be a group and let Autc(G) be the group of central automorphisms of G. We say that a subgroup H of a group G is c-characteristic if α(H) = H for all α ∈ Autc(G). We say that a group G is c-characteristically simple group if it has no non-trivial c-characteristic subgroup. If every subgroup of G is c-characteristic then G is called co-Dedekindian group. In this paper we characterize c-char...

Pentavalent symmetric graphs admitting transitive non-abelian characteristically simple groups

Let Γ be a graph and let G be a group of automorphisms of Γ. The graph Γ is called G-normal if G is normal in the automorphism group of Γ. Let T be a finite non-abelian simple group and let G = T l with l ≥ 1. In this paper we prove that if every connected pentavalent symmetric T -vertex-transitive graph is T -normal, then every connected pentavalent symmetric G-vertex-transitive graph is G-nor...

Unitriangular factorisations of Chevalley groups

On Factorisations of Matrices and Abelian Groups

We establish correspondances between factorisations of finite abelian groups ( direct factors, unitary factors, non isomorphic subgroup classes ) and factorisations of integer matrices. We then study counting functions associated to these factorisations and find average orders. Mathematics Subject Classification 11M41,20K01,15A36.

On Triple Factorisations of Finite Groups

This paper introduces and develops a general framework for studying triple factorisations of the form G = ABA of finite groups G, with A and B subgroups of G. We call such a factorisation nondegenerate if G 6= AB. Consideration of the action of G by right multiplication on the right cosets of B leads to a nontrivial upper bound for |G| by applying results about subsets of restricted movement. F...