Virtual amalgamation of relatively quasiconvex subgroups

Martínez-Pedroza, Eduardo; Sisto, Alessandro

doi:10.2140/agt.2012.12.1993

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Virtual amalgamation of relatively quasiconvex subgroups

Eduardo Martínez-Pedroza and Alessandro Sisto

Algebraic & Geometric Topology 12 (2012) 1993–2002

DOI: 10.2140/agt.2012.12.1993

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 $Q_{1} *_{Q_{1} \cap Q_{2}} Q_{2}$ . 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.

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/

Volume 12, issue 4 (2012)