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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Virtual amalgamation of relatively quasiconvex subgroups

Eduardo Martínez-Pedroza and Alessandro Sisto

Algebraic & Geometric Topology 12 (2012) 1993–2002
Abstract

For relatively hyperbolic groups, we investigate conditions guaranteeing that the subgroup generated by two relatively quasiconvex subgroups Q1 and Q2 is relatively quasiconvex and isomorphic to Q1 Q1Q2Q2. 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.

Keywords
Relatively hyperbolic groups, quasiconvex subgroups, combination theorem, amalgamation, separability
Mathematical Subject Classification 2010
Primary: 20F65, 20F67
References
Publication
Received: 26 March 2012
Revised: 27 June 2012
Accepted: 29 June 2012
Published: 27 October 2012
Authors
Eduardo Martínez-Pedroza
Department of Mathematics and Statistics
Memorial University
Saint John’s
Newfoundland
Canada A1C 5S7
http://www.math.mun.ca/~emartinezped/
Alessandro Sisto
Mathematical Institute
University of Oxford
24-29 St GIles’
Oxford OX1 3LB
UK
http://people.maths.ox.ac.uk/sisto/