Hyperbolic groups and their quotients of bounded exponents

Hyperbolic groups and their quotients of bounded exponents
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双曲群及其有界指数商

DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
A. Olshanskii
A. Olshanskii
中科院分区：
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文献类型：
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作者：
S. Ivanov;A. Olshanskii

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1987年，Gromov证明了对每个非初等双曲群G，存在一个n = n（G）使得商群G/Gn是无限的。文章证实了这一猜想。另外，给出了G/Gn的有限子群的一个刻划，证明了字和共轭问题在G/Gn中可解，且证明了G/Gn中的n ∞ k= 1GK = {1}.证明在很大程度上依赖于以前的作者的结果上的Gromov猜想的挠自由双曲群和伯恩赛德问题的周期群的偶数指数。
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 confirms 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 ⋂∞ k=1G k = {1}. 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.