CYCLIC SUBGROUPS OF EXPONENTIAL-GROWTH AND METRICS ON DISCRETE-GROUPS

Authors
LUBOTZKY A MOZES S RAGHUNATHAN MS
Citation
A. Lubotzky et al., CYCLIC SUBGROUPS OF EXPONENTIAL-GROWTH AND METRICS ON DISCRETE-GROUPS, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 317(8), 1993, pp. 735-740
Citations number
3
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Comptes rendus de l'Academie des sciences. Serie 1, Mathematique → ACNP
ISSN journal
07644442
Volume
317
Issue
8
Year of publication
1993
Pages
735 - 740
Database
ISI
SICI code
0764-4442(1993)317:8<735:CSOEAM>2.0.ZU;2-N
Abstract
Let G be a semi-simple Lie group of rank greater-than-or-equal-to 2 an d GAMMA an irreducible lattice. A cyclic subgroup of GAMMA has exponen tial growth with respect to the generators of GAMMA if and only if it is virtually unipotent. This is used to prove that the word metric of GAMMA is Lipschitz equivalent to the metric induced by the Riemannian metric of G. This confirms a conjecture of D. Kazhdan (cf. Gromov [1]. ).