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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 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.

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Bibliographic databases:
MSC: 16U60, 16S34
Revised: 05.03.2015
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Citation: Ö. Küsmüş, “On the units of integral group ring of $C_{n}\times C_{6}$”, Algebra Discrete Math., 20:1 (2015), 142–151

Citation in format AMSBIB
\Bibitem{Kus15} \by \"O.~K\"usm\"u{\c s} \paper On the units of integral group ring of $C_{n}\times C_{6}$ \jour Algebra Discrete Math. \yr 2015 \vol 20 \issue 1 \pages 142--151 \mathnet{http://mi.mathnet.ru/adm536} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3431956} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000378728700011}