Unit Groups of Some Group Rings

Abstract

Let $RG$ be the gruop ring of the group $G$ over ring $R$ and $\mathcal{U}(RG)$ 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 $T_{3m}=⟨x,y|x^m=y^3=1,x^y=x^t⟩$.

Submitted to Czechoslovak Mathematical Journal

References in corpus (2)

• Which finite simple groups are unit groups?
• The Unit Group of Small Group Algebras and the Minimum Counterexample to the Isomorphism Problem