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...
Saved in:
| Date: | 2018 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
|
| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/789 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| _version_ | 1856543403425136640 |
|---|---|
| author | Nakaoka, Irene N. Rocco, Noraı R. |
| author_facet | Nakaoka, Irene N. Rocco, Noraı R. |
| author_sort | Nakaoka, Irene N. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T08:43:10Z |
| 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 \(G\). |
| first_indexed | 2025-12-02T15:43:21Z |
| format | Article |
| id | admjournalluguniveduua-article-789 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:43:21Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| 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 |
| title | 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_short | A note on semidirect products and nonabelian tensor products of groups |
| title_sort | note on semidirect products and nonabelian tensor products of groups |
| topic | Semidirect products Nonabelian tensor products Frobenius Groups Affine Groups 20J99 20E22 |
| topic_facet | Semidirect products Nonabelian tensor products Frobenius Groups Affine Groups 20J99 20E22 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/789 |
| work_keys_str_mv | AT nakaokairenen anoteonsemidirectproductsandnonabeliantensorproductsofgroups AT rocconoraır anoteonsemidirectproductsandnonabeliantensorproductsofgroups AT nakaokairenen noteonsemidirectproductsandnonabeliantensorproductsofgroups AT rocconoraır noteonsemidirectproductsandnonabeliantensorproductsofgroups |