 
Summary: On Subgroup Separability in Hyperbolic
Coxeter Groups
D. D. LONG1c
and A. W. REID2cc
1
Department of Mathematics, UCSB, Santa Barbara, CA 93106, U.S.A.
2
Department of Mathematics, University of Texas at Austin, Austin, TX 78712, U.S.A.
(Received: 25 May 2000; in ˘nal form: 20 February 2001)
Abstract. We prove that certain hyperbolic Coxeter groups are separable on their geometrically
˘nite subgroups.
Mathematics Subject Classi˘cation (2000). 20H10.
Key words. hyperbolic Coxeter group, subgroup separability.
1. Introduction
Recall that a subgroup H of a group G is separable in G if, given any g P G n H, there
exists a subgroup K ` G of ˘nite index with H ` K and g aP K. G is called subgroup
separable (or LERF) if G is Hsubgroup separable for all ˘nitely generated
H ` G. This powerful property has attracted a good deal of attention in the last
few years, largely motivated by questions which arise in low dimensional topology
(see [1], and [15] for example). In that context, and in the context of negatively curved
