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Finite subgroups of hyperbolic groups. (English. Russian original) Zbl 0901.20022
Algebra Logic 34, No. 6, 343-345 (1995); translation from Algebra Logika 34, No. 6, 619-622 (1995).
Summary: For a hyperbolic group \(G\) with coefficient \(\delta\) with respect to a finite generating set \(X\), it is proved that any finite subgroup of \(G\) is conjugate to a subgroup \(H\) such that each element of \(H\) has length at most \(2\delta+1\) with respect to \(X\).

MSC:
20F65 Geometric group theory
57M07 Topological methods in group theory
20E07 Subgroup theorems; subgroup growth
20F05 Generators, relations, and presentations of groups
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