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
Main Authors:	Nakaoka, Irene N., Rocco, Noraı R.
Format:	Article
Language:	English
Published:	Lugansk National Taras Shevchenko University 2018
Subjects:	Semidirect products Nonabelian tensor products Frobenius Groups Affine Groups 20J99 20E22
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

id	admjournalluguniveduua-article-789
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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
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2018-04-04T08:43:10Z
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
work_keys_str_mv	AT nakaokairenen anoteonsemidirectproductsandnonabeliantensorproductsofgroups AT rocconoraır anoteonsemidirectproductsandnonabeliantensorproductsofgroups AT nakaokairenen noteonsemidirectproductsandnonabeliantensorproductsofgroups AT rocconoraır noteonsemidirectproductsandnonabeliantensorproductsofgroups
first_indexed	2025-12-02T15:43:21Z
last_indexed	2025-12-02T15:43:21Z
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A note on semidirect products and nonabelian tensor products of groups

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