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Periodic quotients of hyperbolic and large groups

By Ashot Minasyan, Alexander Yu. Olshanskii and Dmitriy Sonkin

Abstract

Let G be either a non-elementary (word) hyperbolic group or a large group (both in the sense of Gromov). In this paper we describe several approaches for constructing continuous families of periodic quotients of G with various properties.<br/>The first three methods work for any non-elementary hyperbolic group, producing three different continua of periodic quotients of G. They are based on the results and techniques, that were developed by Ivanov and Olshanskii in order to show that there exists an integer n such that G/G^n is an infinite group of exponent n.<br/>The fourth approach starts with a large group G and produces a continuum of pairwise non-isomorphic periodic residually finite quotients. Speaking of a particular application, we use each of these methods to give a positive answer to a question of Wiegold from Kourovka Notebook

Topics: QA
Year: 2009
OAI identifier: oai:eprints.soton.ac.uk:143197
Provided by: e-Prints Soton

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Citations

  1. (1975). The Burnside Problem and Identities in Groups (Russian), doi

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