On triple factorisations of finite groups

Details On triple factorisations of finite groups On triple factorisations of finite groups

2009-09-24

arxiv.org/abs/0909.4393v1

Mathematics

Group Theory

28 pages

Scientific paper

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 $G\neq AB$. 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. For $A

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