English

Hyperbolic groups and free constructions

Group Theory 2008-02-03 v1

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 Q{\bf Q}-completion of a torsion-free hyperbolic group has solvable word problem and conjugacy problem.

Keywords

Cite

@article{arxiv.math/9605205,
  title  = {Hyperbolic groups and free constructions},
  author = {Olga Kharlampovich and Alexey Myasnikov},
  journal= {arXiv preprint arXiv:math/9605205},
  year   = {2008}
}

Comments

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