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.

MSC: 16U60, 16S34

Received: 21.02.2015
Revised: 05.03.2015

Language: English

Bibliographic databases:

• 
•