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J. London Math. Soc. (2) 73 (2006) 109125 Ce2006 London Mathematical Society doi:10.1112/S002461070502257X
 

Summary: J. London Math. Soc. (2) 73 (2006) 109­125 Ce2006 London Mathematical Society
doi:10.1112/S002461070502257X
A LOWER BOUND ON THE GROWTH OF WORD
HYPERBOLIC GROUPS
G. N. ARZHANTSEVA and I. G. LYSENOK
Abstract
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.
1. Introduction
Let G be a finitely generated group and A a finite set of generators for G. By |x|A
we denote the word length of an element x G in the generators A, that is, the
length of the shortest word in the alphabet A±1
representing x. Let BA(n) denote
the ball {g G | |g|A n} of radius n in G with respect to A. The exponential
growth rate of the pair (G, A) is the limit
(G, A) = lim
n
n
#BA(n).
This limit exists due to the submultiplicativity property of the function #B(n);

  

Source: Arzhantseva, Goulnara N. - Section de Mathématiques, Université de Genève

 

Collections: Mathematics