A note on semidirect products and nonabelian tensor products of groups
Let G and H be groups which act compatibly on one another. In [2] and [8] it is considered a group construction η(G,H) which is related to the nonabelian tensor product G⊗H. In this note we study embedding questions of certain semidirect products A⋊H into η(A,H), for finite abelian H-groups A. As a...
Збережено в:
| Дата: | 2009 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2009
|
| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/154510 |
| 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: | A note on semidirect products and nonabelian tensor products of groups / I.N. Nakaoka, N.R. Rocco // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 3. — С. 77–84. — Бібліогр.: 14 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-154510 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1545102019-06-16T01:27:48Z A note on semidirect products and nonabelian tensor products of groups Nakaoka, I.N. Rocco, N.R. Let G and H be groups which act compatibly on one another. In [2] and [8] it is considered a group construction η(G,H) which is related to the nonabelian tensor product G⊗H. In this note we study embedding questions of certain semidirect products A⋊H into η(A,H), for finite abelian H-groups A. As a consequence of our results we obtain that complete Frobenius groups and affine groups over finite fields are embedded into η(A,H) for convenient groups A and H. Further, on considering finite metabelian groups G in which the derived subgroup has order coprime with its index we establish the order of the nonabelian tensor square of G. 2009 Article A note on semidirect products and nonabelian tensor products of groups / I.N. Nakaoka, N.R. Rocco // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 3. — С. 77–84. — Бібліогр.: 14 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:20J99, 20E22 http://dspace.nbuv.gov.ua/handle/123456789/154510 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 |
Let G and H be groups which act compatibly on one another. In [2] and [8] it is considered a group construction η(G,H) which is related to the nonabelian tensor product G⊗H. In this note we study embedding questions of certain semidirect products A⋊H into η(A,H), for finite abelian H-groups A. As a consequence of our results we obtain that complete Frobenius groups and affine groups over finite fields are embedded into η(A,H) for convenient groups A and H. Further, on considering finite metabelian groups G in which the derived subgroup has order coprime with its index we establish the order of the nonabelian tensor square of G. |
| format |
Article |
| author |
Nakaoka, I.N. Rocco, N.R. |
| spellingShingle |
Nakaoka, I.N. Rocco, N.R. A note on semidirect products and nonabelian tensor products of groups Algebra and Discrete Mathematics |
| author_facet |
Nakaoka, I.N. Rocco, N.R. |
| author_sort |
Nakaoka, I.N. |
| title |
A note on semidirect products and nonabelian tensor products of groups |
| title_short |
A note on semidirect products and nonabelian tensor products of groups |
| title_full |
A note on semidirect products and nonabelian tensor products of groups |
| title_fullStr |
A note on semidirect products and nonabelian tensor products of groups |
| title_full_unstemmed |
A note on semidirect products and nonabelian tensor products of groups |
| title_sort |
note on semidirect products and nonabelian tensor products of groups |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154510 |
| citation_txt |
A note on semidirect products and nonabelian tensor products of groups / I.N. Nakaoka, N.R. Rocco // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 3. — С. 77–84. — Бібліогр.: 14 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT nakaokain anoteonsemidirectproductsandnonabeliantensorproductsofgroups AT rocconr anoteonsemidirectproductsandnonabeliantensorproductsofgroups AT nakaokain noteonsemidirectproductsandnonabeliantensorproductsofgroups AT rocconr noteonsemidirectproductsandnonabeliantensorproductsofgroups |
| first_indexed |
2023-05-20T17:44:38Z |
| last_indexed |
2023-05-20T17:44:38Z |
| _version_ |
1796153987475439616 |