Free subgroups in certain generalized triangle groups of type (2, m, 2)

James Howie, Gerald Williams

Research output: Contribution to journalArticle

Abstract

A generalized triangle group is a group that can be presented in the form G = p = yq = w(x,y)r = 1> where p,q,r = 2 and w(x,y) is a cyclically reduced word of length at least 2 in the free product Zp * Zq = p = yq = 1>. Rosenberger has conjectured that every generalized triangle group G satisfies the Tits alternative. It is known that the conjecture holds except possibly when the triple (p,q,r) is one of (3, 3, 2), (3, 4, 2), (3, 5, 2), or (2, m, 2) where m=3, 4, 5, 6, 10, 12, 15 , 20, 30, 60. In this paper, we show that the Tits alternative holds in the cases (p,q,r)=(2, m, 2) where m=6, 10, 12, 15, 20, 30, 60.

Original languageEnglish
Pages (from-to)181-197
Number of pages17
JournalGeometriae Dedicata
Volume119
Issue number1
DOIs
Publication statusPublished - Apr 2006

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Triangle Group
Subgroup
Free Product
Alternatives
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Keywords

  • Free subgroup
  • Generalised triangle group
  • Tits alternative

Cite this

Howie, James ; Williams, Gerald. / Free subgroups in certain generalized triangle groups of type (2, m, 2). In: Geometriae Dedicata. 2006 ; Vol. 119, No. 1. pp. 181-197.
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Free subgroups in certain generalized triangle groups of type (2, m, 2). / Howie, James; Williams, Gerald.

In: Geometriae Dedicata, Vol. 119, No. 1, 04.2006, p. 181-197.

Research output: Contribution to journalArticle

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