On the units of integral group ring of \(C_{n}\times C_{6}\)
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 \(C_{n}\times C_{6}\) where \(C_{n}=\langle a:a^{n}=1\rangle\) and \(C_{6}=\langle x:x^{6}=1\rangle\). We show that \(\math...
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| Date: | 2015 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2015
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/104 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | 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 \(C_{n}\times C_{6}\) where \(C_{n}=\langle a:a^{n}=1\rangle\) and \(C_{6}=\langle x:x^{6}=1\rangle\). We show that \(\mathcal{U}_{1}(\mathbb{Z}[C_{n}\times C_{6}])\) can be expressed in terms of its 4 subgroups. Furthermore, forms of units in these subgroups are described by the unit group \(\mathcal{U}_{1}(\mathbb{Z}C_{n})\). Notations mostly follow \cite{sehgal2002}. |
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