Growth of periodic quotients of hyperbolic groups

Coulon, Rémi

doi:10.2140/agt.2013.13.3111

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Growth of periodic quotients of hyperbolic groups

Rémi Coulon

Algebraic & Geometric Topology 13 (2013) 3111–3133

DOI: 10.2140/agt.2013.13.3111

Abstract

Let $G$ be a non-elementary torsion-free hyperbolic group. We prove that the exponential growth rate of the periodic quotient $G ∕ G^{n}$ tends to the one of $G$ as $n$ odd approaches infinity. Moreover, we provide an estimate for the rate at which the convergence is taking place.

Keywords

periodic groups, exponential growth, hyperbolic groups

Mathematical Subject Classification 2000

Primary: 20F65

Secondary: 20F50, 20F67, 20F69

References

Publication

Received: 13 December 2012

Revised: 7 May 2013

Accepted: 10 May 2013

Published: 22 August 2013

Authors

Rémi Coulon
Department of Mathematics Vanderbilt University Stevenson Center 1326 Nashville, TN 37240 USA
http://www.math.vanderbilt.edu/~coulonrb/

Volume 13, issue 6 (2013)