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...

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Published in:Algebra and Discrete Mathematics
Date:2009
Main Authors: Nakaoka, I.N., Rocco, N.R.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2009
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/154510
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-154510
record_format dspace
spelling Nakaoka, I.N.
Rocco, N.R.
2019-06-15T16:22:18Z
2019-06-15T16:22:18Z
2009
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
https://nasplib.isofts.kiev.ua/handle/123456789/154510
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.
he authors acknowledge partial financial support from the Brazilian agenciesCNPq (Conselho Nacional de Desenvolvimento Cient ́ıfico e Tecnol ́ogico) and FAPDF(Funda ̧c ̃ao de Apoio `a Pesquisa do Distrito Federal)
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
A note on semidirect products and nonabelian tensor products of groups
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title A note on semidirect products and nonabelian tensor products of groups
spellingShingle A note on semidirect products and nonabelian tensor products of groups
Nakaoka, I.N.
Rocco, N.R.
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
author Nakaoka, I.N.
Rocco, N.R.
author_facet Nakaoka, I.N.
Rocco, N.R.
publishDate 2009
language English
container_title Algebra and Discrete Mathematics
publisher Інститут прикладної математики і механіки НАН України
format Article
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.
issn 1726-3255
url https://nasplib.isofts.kiev.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.
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first_indexed 2025-12-07T13:28:15Z
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