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 language||English (US)|
|Number of pages||48|
|Journal||Transactions of the American Mathematical Society|
|State||Published - 1996|
ASJC Scopus subject areas
- Applied Mathematics