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Growth of periodic quotients of hyperbolic groups. (English) Zbl 1353.20025
Summary: 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.
MSC:
20F65 Geometric group theory
20F50 Periodic groups; locally finite groups
20F67 Hyperbolic groups and nonpositively curved groups
20F69 Asymptotic properties of groups
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