|
Algebra and Discrete Mathematics, 2015, Volume 20, Issue 1, Pages 142–151
(Mi adm536)
|
|
|
|
RESEARCH ARTICLE
On the units of integral group ring of $C_{n}\times C_{6}$
Ö. Küsmüş Department of Mathematics, Faculty of Science, Yuzuncu Yil University
Abstract:
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 [11].
Keywords:
group ring, integral group ring, unit group, unit problem.
Received: 21.02.2015 Revised: 05.03.2015
Citation:
Ö. Küsmüş, “On the units of integral group ring of $C_{n}\times C_{6}$”, Algebra Discrete Math., 20:1 (2015), 142–151
Linking options:
https://www.mathnet.ru/eng/adm536 https://www.mathnet.ru/eng/adm/v20/i1/p142
|
Statistics & downloads: |
Abstract page: | 143 | Full-text PDF : | 72 | References: | 37 |
|