论文标题
中心Socle是理想的组代数
Group algebras in which the socle of the center is an ideal
论文作者
论文摘要
令$ f $为特征$ p> 0 $的字段。我们研究了有限的$ g $的结构，该$ g $ $ fg $的中心是$ fg $中的理想之选，并将有限的$ p $ -groups $ g $与此物业分类。此外，我们对有限组的$ g $进行了明确的描述，为$ fg $的雷诺理想是$ fg $的理想。
Let $F$ be a field of characteristic $p > 0$. We study the structure of the finite groups $G$ for which the socle of the center of $FG$ is an ideal in $FG$ and classify the finite $p$-groups $G$ with this property. Moreover, we give an explicit description of the finite groups $G$ for which the Reynolds ideal of $FG$ is an ideal in $FG$.
