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In 1987, Gromov conjectured that for every non-elementary hy- perbolic group G there is an n = n(G) such that the quotient group G=Gn is innite. The article conrms this conjecture. In addition, a description of nite subgroups of G=Gn is given, it is proven that the word and conjugacy problem are solvable in G=Gn and that T1 k=1G k =f1g. 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.

Hyperbolic groups and their quotients of bounded exponents