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DOI: 10.1007/s00209-002-0434-6 Math. Z. 241, 597611 (2002)

Summary: DOI: 10.1007/s00209-002-0434-6
Math. Z. 241, 597­611 (2002)
Growth tightness for word hyperbolic groups
G. N. Arzhantseva1, I. G. Lysenok2
Section de Math´ematiques, Universit´e de Gen`eve, CP 240, 1211 Gen`eve 24, Switzerland
(e-mail: Goulnara.Arjantseva@math.unige.ch
Steklov Institute of Mathematics, Gubkina str. 8, 117966 Moscow, Russia
(e-mail: lysionok@mi.ras.ru)
Received: 20 September 2001; in final form: 24 January 2002/
Published online: 5 September 2002 ­ c Springer-Verlag 2002
Abstract. Weshowthatnon-elementarywordhyperbolicgroupsaregrowth
tight. This means that, given such a group G and a finite set A of its
generators, for any infinite normal subgroup N of G, the exponential
growth rate of G/N with respect to the natural image of A is strictly less
than the exponential growth rate of G with respect to A.
1. Introduction
Let G be a finitely generated group and A a finite set of generators for G.


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


Collections: Mathematics