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On Triple Factorisations of Finite Groups (2009)
| Citations: | 2 - 1 self |
BibTeX
@MISC{Alavi09ontriple,
author = {S. Hassan Alavi and Cheryl E. Praeger},
title = {On Triple Factorisations of Finite Groups},
year = {2009}
}
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Abstract
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.
