Summary: On Quasiconvex Subgroups of
Word Hyperbolic Groups*
G. N. ARZHANTSEVA
Section de Mathe¨ matiques, Universite¨ de Gene© ve, CP 240, 1211 Geneva 24,
Switzerland. e-mail: email@example.com
(Received: 5 April 2000)
Abstract. We prove that a quasiconvex subgroup H of in¢nite index of a torsion free word
hyperbolic group can be embedded in a larger quasiconvex subgroup which is the free product
of H and an in¢nite cyclic group. Some properties of quasiconvex subgroups of word hyperbolic
group are also discussed.
Mathematics Subject Classi¢cations (2000). 20F32, 20E07, 20E06.
Key words. word hyperbolic groups, quasiconvex subgroups, commensurator.
Word hyperbolic groups were introduced by M. Gromov as a geometric
generalization of certain properties of discrete groups of isometries of hyperbolic
. Finite groups, ¢nitely generated free groups, classical small cancellation
groups and groups acting discretely and cocompactly on hyperbolic spaces are basic
examples of word hyperbolic groups. Any word hyperbolic group is ¢nitely pre-
sented. Finite extensions and free products of ¢nitely many word hyperbolic groups