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On residualizing homomorphisms preserving quasiconvexity

On residualizing homomorphisms preserving quasiconvexity
On residualizing homomorphisms preserving quasiconvexity
H is called a G-subgroup of a hyperbolic group G if for any finite subset M 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.
Word hyperbolic Groups, quasiconvex subsets, residual properties, small cancellation theory.
0092-7872
2423-2463
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d

Minasyan, Ashot (2005) On residualizing homomorphisms preserving quasiconvexity. Communications in Algebra, 33 (7), 2423-2463. (doi:10.1081/AGB-200058383).

Record type: Article

Abstract

H is called a G-subgroup of a hyperbolic group G if for any finite subset M 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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Published date: June 2005
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Keywords: Word hyperbolic Groups, quasiconvex subsets, residual properties, small cancellation theory.

Identifiers

Local EPrints ID: 46727
URI: http://eprints.soton.ac.uk/id/eprint/46727
DOI: doi:10.1081/AGB-200058383
ISSN: 0092-7872
PURE UUID: 7df296ab-b127-481d-8840-c96d4292d7fa
ORCID for Ashot Minasyan: ORCID iD orcid.org/0000-0002-4986-2352

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Date deposited: 17 Jul 2007
Last modified: 16 Mar 2024 03:56

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Author: Ashot Minasyan ORCID iD

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