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Journal of the London Mathematical Society 2006 73(1):109-125; doi:10.1112/S002461070502257X
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© The London Mathematical Society

A Lower Bound on the Growth of Word Hyperbolic Groups

G. N. Arzhantseva and I. G. Lysenok

Section de Mathématiques, Université de Genève CP 64, 1211 Genève 4, Switzerland Goulnara.Arjantseva{at}math.unige.ch
Steklov Institute of Mathematics Gubkina str. 8, 119991 Moscow, Russia lysionok{at}mi.ras.ru

Received 14 September 2003. Revision received 18 March 2004.

We give a linear lower bound on the exponential growth rate of a non-elementary subgroup of a word hyperbolic group, with respect to the number of generators for the subgroup.


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