论文标题
特征两个的交换组代数的统一亚组
Unitary Subgroups of commutative group algebras of characteristic two
论文作者
论文摘要
让$ fg $是有限$ 2 $ -group $ g $的集团代数，这是有限的field $ f $ f $ f $ thtemitiate二和$ \ circledast $ a从$ g $引起的。 $ v _ {\ circledast}（fg）$表示的$ \ circledast $ -UNITAL子组的$ fg $，定义为满足属性$ u^{\ cirdledast} = u^{ - 1} $的所有标准化单位$ u $的集合。 In this paper we establish the order of $V_{\circledast}(FG)$ for all involutions $\circledast$ which arise from $G$, where $G$ is a finite cyclic $2$-group and show that all $\circledast$-unitary subgroups of $FG$ are not isomorphic.
Let $FG$ be the group algebra of a finite $2$-group $G$ over a finite field $F$ of characteristic two and $\circledast$ an involution which arises from $G$. The $\circledast$-unitary subgroup of $FG$, denoted by $V_{\circledast}(FG)$, is defined to be the set of all normalized units $u$ satisfying the property $u^{\circledast}=u^{-1}$. In this paper we establish the order of $V_{\circledast}(FG)$ for all involutions $\circledast$ which arise from $G$, where $G$ is a finite cyclic $2$-group and show that all $\circledast$-unitary subgroups of $FG$ are not isomorphic.
