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ON QUASICONVEX SUBGROUPS OF WORD HYPERBOLIC G. N. ARZHANTSEVA
 

Summary: ON QUASICONVEX SUBGROUPS OF WORD HYPERBOLIC
GROUPS
G. N. ARZHANTSEVA
Abstract. We prove that a quasiconvex subgroup H of infinite 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 infinite cyclic group. Some
properties of quasiconvex subgroups of word hyperbolic group are also dis­
cussed.
1. Introduction
Word hyperbolic groups were introduced by M. Gromov as a geometric gener­
alization of certain properties of discrete groups of isometries of hyperbolic spaces
H n . Finite groups, finitely generated free groups, classical small cancellation groups
and groups acting discretely and cocompactly on hyperbolic spaces are basic exam­
ples of word hyperbolic groups. Any word hyperbolic group is finitely presented.
Finite extensions and free products of finitely many word hyperbolic groups are
also word hyperbolic. A large number of results on word hyperbolic groups as well
as conjectures and research problems are contained in the original article [9].
In this paper, we study properties of quasiconvex subgroups of word hyperbolic
groups (see the next section for the definition). Our main result gives in fact a
method for constructing quasiconvex subgroups of word hyperbolic groups.

  

Source: Arzhantseva, Goulnara N. - Section de Mathématiques, Université de Genève

 

Collections: Mathematics