Volume 13, issue 6 (2013)

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Growth of periodic quotients of hyperbolic groups

Rémi Coulon

Algebraic & Geometric Topology 13 (2013) 3111–3133
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