Hyperbolic groups and free constructions

Details Hyperbolic groups and free constructions Hyperbolic groups and free constructions

1996-05-13

arxiv.org/abs/math/9605205v1

Mathematics

Group Theory

LaTex file, 44 pages. To appear in Trans. Am. Math. Soc

Scientific paper

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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