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Greenberg's Theorem for Quasiconvex Subgroups of Word Hyperbolic Groups

Published online by Cambridge University Press:  20 November 2018

Ilya Kapovich  and
Hamish Short
Ilya Kapovich
Affiliation:
City College, 138th Street and Convent Avenue, New York, NY, USA 10031 e-mail: ilya@groups.sci.ccny.cuny.edu
Hamish Short
Affiliation:
C.M.I., Université de Provence, 39 Rue Joliot-Curie, 13452 Marseille Cedex 13, France e-mail: hamish@claudia.univ-mrs.fr
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Abstract

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Analogues of a theorem of Greenberg about finitely generated subgroups of free groups are proved for quasiconvex subgroups of word hyperbolic groups. It is shown that a quasiconvex subgroup of a word hyperbolic group is a finite index subgroup of only finitely many other subgroups.

Keywords

20F3257Mword hyperbolic groupboundaryquasiconvex
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 6 , 01 December 1996 , pp. 1224 - 1244
Copyright
Copyright © Canadian Mathematical Society 1996

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