Geodesic
Virtual amalgamation of relatively quasiconvex subgroups
Martínez-Pedroza, Eduardo1 ; Sisto, Alessandro2
1Department of Mathematics and Statistics, Memorial University, Saint John’s, Newfoundland, Canada A1C 5S7
2Mathematical Institute, University of Oxford, 24-29 St GIles’, Oxford OX1 3LB, UK
Algebraic and Geometric Topology, Tome 12 (2012) no. 4, pp. 1993-2002
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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 ∗Q1∩Q2Q2. 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.

DOI : 10.2140/agt.2012.12.1993
Classification : 20F65, 20F67
Keywords: Relatively hyperbolic groups, quasiconvex subgroups, combination theorem, amalgamation, separability

Martínez-Pedroza, Eduardo  1   ; Sisto, Alessandro  2

1 Department of Mathematics and Statistics, Memorial University, Saint John’s, Newfoundland, Canada A1C 5S7
2 Mathematical Institute, University of Oxford, 24-29 St GIles’, Oxford OX1 3LB, UK 
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Martínez-Pedroza, Eduardo; Sisto, Alessandro. Virtual amalgamation of relatively quasiconvex subgroups. Algebraic and Geometric Topology, Tome 12 (2012) no. 4, pp. 1993-2002. doi: 10.2140/agt.2012.12.1993

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