Quasiconvexity and amalgams

Ilya Kapovich

Research output: Contribution to journalArticlepeer-review


We obtain a criterion for quasiconvexity of a subgroup of an amalgamated free product of two word hyperbolic groups along a virtually cyclic subgroup. The result provides a method of constructing new word hyperbolic group in class (Q), that is such that all their finitely generated subgroups are quasiconvex. It is known that free groups, hyperbolic surface groups and most 3-dimensional Kleinian groups have property (Q). We also give some applications of our results to one-relator groups and exponential groups.

Original languageEnglish (US)
Pages (from-to)771-811
Number of pages41
JournalInternational Journal of Algebra and Computation
Issue number6
StatePublished - Dec 1997
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


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