Generating groups by conjugation-invariant sets

2011/05/30 by Bardakov, Valery, Tolstykh, Vladimir, Vershinin, Vladimir
#20F05 (20F65) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1105.5844

Abstract

Let S be a generating set of a group G. We say that G has FINITE WIDTH relative to S if G=(S∪ S^-1)^k for a suitable natural number k. We say that a group G is a group of FINITE C-WIDTH if G has finite width with respect to all conjugation-invariant generating sets. We give a number of examples of groups of finite C-width, and, in particular, we prove that the commutator subgroup F' of Thompson's group F is a group of finite C-width. We also study the behaviour of the class of all groups of finite C-width under some group-theoretic constructions; it is established, for instance, that this class is closed under formation of group extensions.

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