Article Dans Une Revue Journal of Algebra and Its Applications Année : 2011

Generating groups by conjugation-invariant sets

Résumé

Let S be a generating set of a group G. We say that G has FINITE WIDTH relative to S if G=(S\cup 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.

Dates et versions

hal-00818615 , version 1 (28-04-2013)

Identifiants

Citer

Valery Bardakov, Vladimir Tolstykh, Vladimir Vershinin. Generating groups by conjugation-invariant sets. Journal of Algebra and Its Applications, 2011, 11, pp.1250071. ⟨10.1142/S0219498812500715⟩. ⟨hal-00818615⟩
86 Consultations
0 Téléchargements

Altmetric

Partager

  • More