 
Summary: DOI: 10.1007/s0020900204346
Math. Z. 241, 597611 (2002)
MathematischeZeitschrift
Growth tightness for word hyperbolic groups
G. N. Arzhantseva1, I. G. Lysenok2
1
Section de Math´ematiques, Universit´e de Gen`eve, CP 240, 1211 Gen`eve 24, Switzerland
(email: Goulnara.Arjantseva@math.unige.ch
2
Steklov Institute of Mathematics, Gubkina str. 8, 117966 Moscow, Russia
(email: lysionok@mi.ras.ru)
Received: 20 September 2001; in final form: 24 January 2002/
Published online: 5 September 2002 c SpringerVerlag 2002
Abstract. Weshowthatnonelementarywordhyperbolicgroupsaregrowth
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.
