Unit Groups of Some Group Rings

Let \(RG\) be the gruop ring of the group \(G\) over ring \(R\) and \(\mathscr{U}(RG)\) be its unit group. Finding the structure of the unit group of a finite group ring is an old topic in ring theory. In, G. Tang et al: Unit Groups of Group Algebras of Some Small Groups. Czech. Math. J. 64 (2014),...

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Bibliographic Details
Published inarXiv.org
Main Author Ashja', Ali
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 06.04.2020
Subjects
Fields (mathematics)
Group theory
Rings (mathematics)
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Summary:Let \(RG\) be the gruop ring of the group \(G\) over ring \(R\) and \(\mathscr{U}(RG)\) be its unit group. Finding the structure of the unit group of a finite group ring is an old topic in ring theory. In, G. Tang et al: Unit Groups of Group Algebras of Some Small Groups. Czech. Math. J. 64 (2014), 149--157, the structure of the unit group of the group ring of the non abelian group \(G\) with order \(21\) over any finite field of characteristic 3 was established. In this paper, we are going to generalize their result to any non abelian group \(G=T_{3m}\), where \(T_{3m} = \langle x,y\,|\,x^m=y^3=1,\,x^y=x^t\rangle\).
ISSN:2331-8422