Product set growth in Burnside groups

Rémi Coulon; Markus Steenbock

doi:10.5802/jep.187

Rémi Coulon ¹; Markus Steenbock ²

¹ IRMAR, Univ Rennes et CNRS 35000 Rennes, France
² Fakultät für Mathematik, Universität Wien 1090 Wien, Austria

Journal de l’École polytechnique — Mathématiques, Volume 9 (2022), pp. 463-504.

Abstract
Résumé

Given a periodic quotient of a torsion-free hyperbolic group, we provide a fine lower estimate of the growth function of any sub-semi-group. This generalizes results of Razborov and Safin for free groups.

Étant donné un quotient périodique d’un groupe hyperbolique sans torsion, nous donnons une estimation inférieure fine de la fonction de croissance pour chacun de tous ses sous-semi-groupes. Cet énoncé généralise des résultats de Razborov et Safin pour les groupes libres.

Received: 2021-02-26
Accepted: 2022-02-15
Published online: 2022-02-28

DOI: 10.5802/jep.187

Classification: 20F65, 20F67, 20F50, 20F06, 20F69
Keywords: Product sets, growth, hyperbolic groups, acylindrical actions, small cancellation, infinite periodic groups, Burnside problem
Mot clés : Ensemble produit, croissance, groupes hyperboliques, actions cylindriques, théorie de la petite simplification, groupes périodiques infinis, problème de Burnside

Author's affiliations:

Rémi Coulon ¹; Markus Steenbock ²

¹ IRMAR, Univ Rennes et CNRS 35000 Rennes, France
² Fakultät für Mathematik, Universität Wien 1090 Wien, Austria

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {R\'emi Coulon and Markus Steenbock},
     title = {Product set growth in {Burnside} groups},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
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Rémi Coulon; Markus Steenbock. Product set growth in Burnside groups. Journal de l’École polytechnique — Mathématiques, Volume 9 (2022), pp. 463-504. doi : 10.5802/jep.187. https://jep.centre-mersenne.org/articles/10.5802/jep.187/

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