论文标题
一些组环的单位组
Unit Groups of Some Group Rings
论文作者
论文摘要
令$ rg $为环$ r $和$ \ mathscr {u}（rg）$是其单位组的Group $ g $的GRUOP环。找到有限组环的单位组的结构是环理论中的一个旧话题。在G. Tang等人中：一些小组的代数组组组。捷克。数学。 J. 64（2014），149--157，非Abelian Group $ G $的组圈的结构，订单$ 21 $在任何有限特征3的领域都建立了。在本文中，我们将把它们的结果推广到任何非Abelian组$ g = t_ {3m} $，其中$ t_ {3m} = \ langle x，y \，| \，| \，x^m = y^3 = 1，\，\，x^y = x^t \ rangle $。
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 $T_{3m} = \langle x,y\,|\,x^m=y^3=1,\,x^y=x^t\rangle$.
