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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2009 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2009
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/154510 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862622966980804608 |
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| author | Nakaoka, I.N. Rocco, N.R. |
| author_facet | Nakaoka, I.N. Rocco, N.R. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-07T13:28:15Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-154510 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T13:28:15Z |
| publishDate | 2009 |
| publisher | Інститут прикладної математики і механіки НАН України |
| 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 |
| spellingShingle | A note on semidirect products and nonabelian tensor products of groups Nakaoka, I.N. Rocco, N.R. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154510 |
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