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 \(\eta(G,H)\) which is related to the nonabelian tensor product \(G \otimes H\). In this note we study embedding questions of certain semidirect products \(A \rtimes H\) into \(\et...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/789 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-7892018-04-04T08:43:10Z A note on semidirect products and nonabelian tensor products of groups Nakaoka, Irene N. Rocco, Noraı R. Semidirect products, Nonabelian tensor products, Frobenius Groups, Affine Groups 20J99, 20E22 Let \(G\) and \(H\) be groups which act compatibly on one another. In [2] and [8] it is considered a group construction \(\eta(G,H)\) which is related to the nonabelian tensor product \(G \otimes H\). In this note we study embedding questions of certain semidirect products \(A \rtimes H\) into \(\eta(A, H)\), 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 \(\eta(A, H)\) 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 \(G\). Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/789 Algebra and Discrete Mathematics; Vol 8, No 3 (2009) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/789/319 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
Semidirect products Nonabelian tensor products Frobenius Groups Affine Groups 20J99 20E22 |
| spellingShingle |
Semidirect products Nonabelian tensor products Frobenius Groups Affine Groups 20J99 20E22 Nakaoka, Irene N. Rocco, Noraı R. A note on semidirect products and nonabelian tensor products of groups |
| topic_facet |
Semidirect products Nonabelian tensor products Frobenius Groups Affine Groups 20J99 20E22 |
| format |
Article |
| author |
Nakaoka, Irene N. Rocco, Noraı R. |
| author_facet |
Nakaoka, Irene N. Rocco, Noraı R. |
| author_sort |
Nakaoka, Irene 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 |
| description |
Let \(G\) and \(H\) be groups which act compatibly on one another. In [2] and [8] it is considered a group construction \(\eta(G,H)\) which is related to the nonabelian tensor product \(G \otimes H\). In this note we study embedding questions of certain semidirect products \(A \rtimes H\) into \(\eta(A, H)\), 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 \(\eta(A, H)\) 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 \(G\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/789 |
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2024-04-12T06:26:18Z |
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