Unit Groups of Some Group Rings

2020/04/06 by Ashja', Ali
#16S34 (Primary) 20C05 #16U60 (Secondary) #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2004.03026

Abstract

Let RG be the gruop ring of the group G over ring R and \mathscrU(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=y³=1, x^y=x^t⟩.

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