Free Subgroups in Certain Generalized Triangle Groups of Type (2, m, 2) |
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Authors: | James Howie Gerald Williams |
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Institution: | (1) School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK;(2) Institute of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent, CT2 7NF, UK |
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Abstract: | A generalized triangle group is a group that can be presented in the form where p,q,r ≥ 2 and w(x,y) is a cyclically reduced word of length at least 2 in the free product . 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. |
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Keywords: | Generalised triangle group Free subgroup Tits alternative |
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