论文标题
在组代数的统一亚组上
On the Unitary Subgroups of group algebras
论文作者
论文摘要
让$ fg $是有限$ p $ -group $ g $在有限场$ f $ f $ p $ p $和$*$的$ fg $的经典互动上的团体代数。 $*$ - $ fg $的统一子组，用$ v _*（fg）$表示为满足属性$ u^*= u^{ - 1} $的所有标准化单元的集合。在本文中，我们提供了一种递归方法，如何计算许多非交通性组代数的$*$ - 单一子组的顺序。我们还证明了组代数的模块化同构问题的一个变体，其中$ f $是特征两个的有限领域，即$ v _*（fg）$确定所有非亚伯利亚$ 2 $ 2 $ - groups $ g $ g $ g $ g $ g $ g $ g $ g $的基本$ g $。
Let $FG$ be the group algebra of a finite $p$-group $G$ over a finite field $F$ of characteristic $p$ and $*$ the classical involution of $FG$. The $*$-unitary subgroup of $FG$, denoted by $V_*(FG)$, is defined to be the set of all normalized units $u$ satisfying the property $u^*=u^{-1}$. In this paper we give a recursive method how to compute the order of the $*$-unitary subgroup for many non-commutative group algebras. We also prove a variant of the modular isomorphism question of group algebras, where $F$ is a finite field of characteristic two, that is $V_*(FG)$ determines the basic group $G$ for all non-abelian $2$-groups $G$ of order at most $2^4$.
