The Tits alternative for generalized triangle groups of type (3,4,2)
A generalized triangle group is a group that can be presented in the form G=⟨x,y |xp=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=⟨x,y |xp=yq=1⟩. Rosenberger has conjectured that every generalized triangle group G satisfies the Ti...
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| Date: | 2008 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2008
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/153357 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The Tits alternative for generalized triangle groups of type (3,4,2) / J. Howie, G. Williams // Algebra and Discrete Mathematics. — 2008. — Vol. 7, № 4. — С. 40–48. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | A generalized triangle group is a group that can be presented in the form G=⟨x,y |xp=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=⟨x,y |xp=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 (2,3,2), (2,4,2), (2,5,2), (3,3,2), (3,4,2), or (3,5,2). Building on a result of Benyash-Krivets and Barkovich from this journal, we show that the Tits alternative holds in the case (p,q,r)=(3,4,2). |
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