Hyperbolic groups and free constructions

O. Kharlampovich, A. Myasnikov

Research output: Contribution to journalArticlepeer-review

66 Scopus citations

Abstract

It is proved that the property of a group to be hyperbolic is preserved under HHN-extensions and amalgamated free products provided the associated (amalgamated) subgroups satisfy certain conditions. Some more general results about the preservation of hyperbolicity under graph products are also obtained. Using these results we describe the Q-completion (Q is the field of rationals) GQ of a torsion-free hyperbolic group G as a union of an effective chain of hyperbolic subgroups, and solve the conjugacy problem in GQ.

Original languageEnglish
Pages (from-to)571-613
Number of pages43
JournalTransactions of the American Mathematical Society
Volume350
Issue number2
DOIs
StatePublished - 1998

Fingerprint

Dive into the research topics of 'Hyperbolic groups and free constructions'. Together they form a unique fingerprint.

Cite this