On the units of integral group ring of Cn×C₆
There are many kind of open problems with varying difficulty on units in a given integral group ring. In this note, we characterize the unit group of the integral group ring of Cn×C₆ where Cn=⟨a:aⁿ=1⟩ and C₆=⟨x:x⁶=1⟩. We show that U₁(Z[Cn×C₆]) can be expressed in terms of its 4 subgroups. Furthermor...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2015 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154754 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On the units of integral group ring of Cn×C₆ / Ö. Küsmüş // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 2. — С. 142-151. — Бібліогр.: 11 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862574661136547840 |
|---|---|
| author | Küsmüş, Ö. |
| author_facet | Küsmüş, Ö. |
| citation_txt | On the units of integral group ring of Cn×C₆ / Ö. Küsmüş // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 2. — С. 142-151. — Бібліогр.: 11 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | There are many kind of open problems with varying difficulty on units in a given integral group ring. In this note, we characterize the unit group of the integral group ring of Cn×C₆ where Cn=⟨a:aⁿ=1⟩ and C₆=⟨x:x⁶=1⟩. We show that U₁(Z[Cn×C₆]) can be expressed in terms of its 4 subgroups. Furthermore, forms of units in these subgroups are described by the unit group U₁(ZCn).
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| first_indexed | 2025-11-26T10:17:37Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154754 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-26T10:17:37Z |
| publishDate | 2015 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Küsmüş, Ö. 2019-06-15T19:58:39Z 2019-06-15T19:58:39Z 2015 On the units of integral group ring of Cn×C₆ / Ö. Küsmüş // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 2. — С. 142-151. — Бібліогр.: 11 назв. — англ. 1726-3255 2010 MSC:16U60, 16S34. https://nasplib.isofts.kiev.ua/handle/123456789/154754 There are many kind of open problems with varying difficulty on units in a given integral group ring. In this note, we characterize the unit group of the integral group ring of Cn×C₆ where Cn=⟨a:aⁿ=1⟩ and C₆=⟨x:x⁶=1⟩. We show that U₁(Z[Cn×C₆]) can be expressed in terms of its 4 subgroups. Furthermore, forms of units in these subgroups are described by the unit group U₁(ZCn). The authors would like to thank to all the members of the journal Algebra and Discrete Mathematics. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On the units of integral group ring of Cn×C₆ Article published earlier |
| spellingShingle | On the units of integral group ring of Cn×C₆ Küsmüş, Ö. |
| title | On the units of integral group ring of Cn×C₆ |
| title_full | On the units of integral group ring of Cn×C₆ |
| title_fullStr | On the units of integral group ring of Cn×C₆ |
| title_full_unstemmed | On the units of integral group ring of Cn×C₆ |
| title_short | On the units of integral group ring of Cn×C₆ |
| title_sort | on the units of integral group ring of cn×c₆ |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154754 |
| work_keys_str_mv | AT kusmuso ontheunitsofintegralgroupringofcnc6 |