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Algebra and Discrete Mathematics, 2004, Issue 2, Pages 23–44
(Mi adm336)
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This article is cited in 1 scientific paper (total in 1 paper)
RESEARCH ARTICLE
On the Tits alternative for some generalized triangle groups
Valery Beniash-Kryvetsa, Oxana Barkovichb a Department of Algebra,
Byelorussian State University, 4, F. Skaryny Ave., 220050, Minsk, Belarus
b Department of Algebra and Geometry, Byelorussian State Pedagogical University, Minsk, Belarus
Abstract:
One says that the Tits alternative holds for a finitely generated group $\Gamma$ if $\Gamma$ contains either a non abelian free subgroup or a solvable subgroup of finite index. Rosenberger states the conjecture that the Tits alternative holds for generalized triangle groups $T(k,l,m,R)=\langle a,b; a^k=b^l=R^m(a,b)=1\rangle$. In the paper Rosenberger's conjecture is proved for groups $T(2,l,2,R)$ with $l=6,12,30,60$ and some special groups $T(3,4,2,R)$.
Keywords:
Tits alternative, generalized triangle group, free subgroup.
Received: 24.02.2004 Revised: 01.06.2004
Citation:
Valery Beniash-Kryvets, Oxana Barkovich, “On the Tits alternative for some generalized triangle groups”, Algebra Discrete Math., 2004, no. 2, 23–44
Linking options:
https://www.mathnet.ru/eng/adm336 https://www.mathnet.ru/eng/adm/y2004/i2/p23
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