Hyperbolic groups and their quotients of bounded exponents

S. V. Ivanov, A. Yu Ol'shanskii

Research output: Contribution to journalArticlepeer-review


In 1987, Gromov conjectured that for every non-elementary hyperbolic group G there is an n = n(G) such that the quotient group G/Gn is infinite. The article conforms this conjecture. In addition, a description of finite subgroups of G/Gn is given, it is proven that the word and conjugacy problem are solvable in G/Gn and that (formula presented). The proofs heavily depend upon prior authors' results on the Gromov conjecture for torsion free hyperbolic groups and on the Burnside problem for periodic groups of even exponents.

Original languageEnglish (US)
Pages (from-to)2091-2138
Number of pages48
JournalTransactions of the American Mathematical Society
Issue number6
StatePublished - 1996

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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