On the engulfing property for word hyperbolic groups
by
Ashot Minasyan
University of Geneva

A group G engulfs its subgroup H, if there exists a proper finite index subgroup K £ G such that H £ K. We will say that a hyperbolic group has the Engulfing Property if it engulfs every proper quasiconvex subgroup.

Let G be a group satisfying the Engulfing Property. We prove that each quasiconvex subgroup H £ G has a finite index in its profinite closure H^* in G. If, in addition, G is residually finite (or torsion-free) we show that H^*=H. In particular, this generalizes results of D. Long and G. Niblo-B. Williams.

Date received: January 21, 2006