Free subgroups in certain generalized triangle groups of type (2, m, 2)
نویسندگان
چکیده
A generalized triangle group is a group that can be presented in the form G = 〈 x, y | x = y = w(x, y) = 1 〉 where p, q, r ≥ 2 and w(x, y) is an element of the free product 〈 x, y | x = y = 1 〉 involving both x and y. 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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