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Bulletin of the London Mathematical Society 2008 40(1):57-64; doi:10.1112/blms/bdm092
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© 2008 London Mathematical Society

The Tits alternative for non-spherical Pride groups

Natalia Kopteva

Sobolev Institute of Mathematics
Academician Koptyug's avenue
4 Novosibirsk 630090
Russia
natasha@math.nsc.ru

Gerald Williams

Institute of Mathematics, Statistics and Actuarial Science
University of Kent
Canterbury
CT2 7NF
United Kingdom

Received 24 July 2006. Revision received 20 March 2007.

Pride groups, or ‘groups given by presentations in which each defining relator involves at most two types of generators’, include Coxeter groups, Artin groups, triangles of groups, and Vinberg's groups defined by periodic paired relations. We show that every non-spherical Pride group that is not a triangle of groups satisfies the Tits alternative.

2000 Mathematics Subject Classification 20E05 (primary), 20E07, 20F05, 20F06 (secondary).

The first author was partially supported by an FP6 Marie Curie IIF Fellowship.


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