On the Tits alternative for some generalized triangle groups
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...
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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/988 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | 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 \(T(3,4,2,R)\). |
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