2009/09/24 by S. Hassan Alavi, Cheryl E. Praeger, Alavi, S. Hassan +1
Mathematics · #20B05 (primary) #20B15 #20D40 (secondary) #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20B05 #msc:20B15 #msc:20D40
paper · pdf · doi:10.48550/arxiv.0909.4393
28 pages
arxiv created 2009/09/24 · arxiv updated 2009/12/01
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≠ 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<C<G and B<D<G the factorisation G=CDC may be degenerate even if G=ABA is nondegenerate. Similarly forming quotients may lead to degenerate triple factorisations. A rationale is given for reducing the study of nondegenerate triple factorisations to those in which G acts faithfully and primitively on the cosets of A. This involves study of a wreath product construction for triple factorisations.