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Article Dans Une Revue Bulletin de la société mathématique de France Année : 2018

Detecting trivial elements of periodic groups

Un critère pour détecter les éléments triviaux dans un quotient périodique d'un groupe hyperbolique

Résumé

In this article we give a sufficient and necessary condition to determine wether or not an element of the free group induces a non-trivial element of the free Burnside group of sufficiently large odd exponent. This criterion can be stated without any knowledge about Burnside groups, in particular about the proof of its infiniteness. Therefore it provides a useful tool that we will use later to study outer automorphisms of Burnside groups. We also state an analogue result for periodic quotients of torsion-free hyperbolic groups.

Dates et versions

hal-01662863 , version 1 (13-12-2017)

Identifiants

Citer

Rémi Coulon. Detecting trivial elements of periodic groups. Bulletin de la société mathématique de France, 2018, 146 (4), pp.745-806. ⟨10.24033/bsmf.2772⟩. ⟨hal-01662863⟩
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