On Residualizing Homomorphisms Preserving Quasiconvexity

Details On Residualizing Homomorphisms Preserving Quasiconvexity On Residualizing Homomorphisms Preserving Quasiconvexity

2004-06-07

arxiv.org/abs/math/0406126v2

Comm. in Algebra 33 (2005), no. 7, pp. 2423-2463

Mathematics

Group Theory

41 pages, 2 figures. Final version (some typos corrected)

Scientific paper

$H$ is called a $G$-subgroup of a hyperbolic group $G$ if for any finite subset $M\subset G$ there exists a homomorphism from $G$ onto a non-elementary hyperbolic group $G_1$ 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 $G$. Here 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.

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