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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Growth of relatively hyperbolic groups


Author: Xiangdong Xie
Journal: Proc. Amer. Math. Soc. 135 (2007), 695-704
MSC (2000): Primary 20F65
Published electronically: September 15, 2006
MathSciNet review: 2262865
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Abstract: We show that a finitely generated group that is hyperbolic relative to a collection of proper subgroups either is virtually cyclic or has uniform exponential growth.


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Additional Information

Xiangdong Xie
Affiliation: Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221
Address at time of publication: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123
Email: xxie@math.uc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08537-6
PII: S 0002-9939(06)08537-6
Keywords: Exponential growth, uniform exponential growth, relatively hyperbolic groups, geometrically finite groups.
Received by editor(s): April 10, 2005
Received by editor(s) in revised form: October 18, 2005
Published electronically: September 15, 2006
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.