On residualizing homomorphisms preserving quasiconvexity
by
Ashot Minasyan
Vanderbilt University, Nashville, Tennessee

H is called a G-subgroup of a hyperbolic group G if for any finite subset M of G there exists a homomorphism from G onto a non-elementary hyperbolic group G₁ that is surjective on H and injective on M. In his paper in 1993 A. Ol'shanskii gave a description of all G-subgroups in any given non-elementary hyperbolic group G. We show that for the same class of G-subgroups the finiteness assumption on M (under certain natural conditions) can be replaced by an assumption of quasiconvexity. Thereafter we use this result to obtain new embedding theorems for hyperbolic groups.

Paper reference: arXiv:math.GR/0406126

Date received: September 7, 2004