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Hyperbolic groups and free constructions

Olga Kharlampovich·Alexey Myasnikov
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Abstract

We investigate which free constructions (amalgamated products and HNN-extensions) over word hyperbolic groups produce groups that are again word hyperbolic. A complete answer is obtained for the case when the amalgamated subgroups are virtually cyclic. The results are applied, in particular, to show that a ${\bf Q}$-completion of a torsion-free hyperbolic group has solvable word problem and conjugacy problem.

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Olga Kharlampovich, Alexey Myasnikov. 1996-05-13. Hyperbolic groups and free constructions. https://arxiv.org/abs/math/9605205

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