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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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/789 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | 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 \(G\). |
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