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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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2008 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2008
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| Online Access: | https://nasplib.isofts.kiev.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| _version_ | 1862726893974847488 |
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| author | Howie, J. Williams, G. |
| author_facet | Howie, J. Williams, G. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | 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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| first_indexed | 2025-12-07T19:00:07Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-153357 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T19:00:07Z |
| publishDate | 2008 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Howie, J. Williams, G. 2019-06-14T03:34:25Z 2019-06-14T03:34:25Z 2008 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. 1726-3255 2000 Mathematics Subject Classification: 20F05, 20E05, 57M07. https://nasplib.isofts.kiev.ua/handle/123456789/153357 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). en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics The Tits alternative for generalized triangle groups of type (3,4,2) Article published earlier |
| spellingShingle | The Tits alternative for generalized triangle groups of type (3,4,2) Howie, J. Williams, G. |
| title | The Tits alternative for generalized triangle groups of type (3,4,2) |
| title_full | The Tits alternative for generalized triangle groups of type (3,4,2) |
| title_fullStr | The Tits alternative for generalized triangle groups of type (3,4,2) |
| title_full_unstemmed | The Tits alternative for generalized triangle groups of type (3,4,2) |
| title_short | The Tits alternative for generalized triangle groups of type (3,4,2) |
| title_sort | tits alternative for generalized triangle groups of type (3,4,2) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/153357 |
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