Virtual amalgamation of relatively quasiconvex subgroups

Eduardo Martínez-Pedroza; Alessandro Sisto

doi:10.2140/agt.2012.12.1993

Virtual amalgamation of relatively quasiconvex subgroups

Eduardo Martínez-Pedroza^*, Alessandro Sisto

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

For relatively hyperbolic groups, we investigate conditions guaranteeing that the subgroup generated by two relatively quasiconvex subgroups Q ₁ and Q ₂ is relatively quasiconvex and isomorphic to Q ₁* Q ₁∩Q2 Q ₂. The main theorem extends results for quasiconvex subgroups of word-hyperbolic groups, and results for discrete subgroups of isometries of hyperbolic spaces. An application on separability of double cosets of quasiconvex subgroups is included.

Original language	English
Pages (from-to)	1993-2002
Number of pages	10
Journal	Algebraic and Geometric Topology
Volume	12
Issue number	4
DOIs	https://doi.org/10.2140/agt.2012.12.1993
Publication status	Published - 27 Oct 2012

ASJC Scopus subject areas

Geometry and Topology

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10.2140/agt.2012.12.1993

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AU - Martínez-Pedroza, Eduardo

AU - Sisto, Alessandro

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N2 - For relatively hyperbolic groups, we investigate conditions guaranteeing that the subgroup generated by two relatively quasiconvex subgroups Q 1 and Q 2 is relatively quasiconvex and isomorphic to Q 1* Q 1∩Q2 Q 2. The main theorem extends results for quasiconvex subgroups of word-hyperbolic groups, and results for discrete subgroups of isometries of hyperbolic spaces. An application on separability of double cosets of quasiconvex subgroups is included.

AB - For relatively hyperbolic groups, we investigate conditions guaranteeing that the subgroup generated by two relatively quasiconvex subgroups Q 1 and Q 2 is relatively quasiconvex and isomorphic to Q 1* Q 1∩Q2 Q 2. The main theorem extends results for quasiconvex subgroups of word-hyperbolic groups, and results for discrete subgroups of isometries of hyperbolic spaces. An application on separability of double cosets of quasiconvex subgroups is included.

UR - http://www.scopus.com/inward/record.url?scp=84868531892&partnerID=8YFLogxK

U2 - 10.2140/agt.2012.12.1993

DO - 10.2140/agt.2012.12.1993

M3 - Article

AN - SCOPUS:84868531892

SN - 1472-2747

VL - 12

SP - 1993

EP - 2002

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 4

ER -

Virtual amalgamation of relatively quasiconvex subgroups

Abstract

ASJC Scopus subject areas

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