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...
Збережено в:
| Дата: | 2008 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2008
|
| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/153357 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-153357 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1533572019-06-15T01:26:40Z The Tits alternative for generalized triangle groups of type (3,4,2) Howie, J. Williams, G. 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). 2008 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/153357 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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). |
| format |
Article |
| author |
Howie, J. Williams, G. |
| spellingShingle |
Howie, J. Williams, G. The Tits alternative for generalized triangle groups of type (3,4,2) Algebra and Discrete Mathematics |
| author_facet |
Howie, J. Williams, G. |
| author_sort |
Howie, J. |
| title |
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_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_sort |
tits alternative for generalized triangle groups of type (3,4,2) |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/153357 |
| 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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT howiej thetitsalternativeforgeneralizedtrianglegroupsoftype342 AT williamsg thetitsalternativeforgeneralizedtrianglegroupsoftype342 AT howiej titsalternativeforgeneralizedtrianglegroupsoftype342 AT williamsg titsalternativeforgeneralizedtrianglegroupsoftype342 |
| first_indexed |
2023-05-20T17:38:44Z |
| last_indexed |
2023-05-20T17:38:44Z |
| _version_ |
1796153768514945024 |