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arXiv · 2212.01601

Group algebras in which the socle of the center is an ideal

Sofia Brenner·Burkhard Külshammer
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Abstract

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 $FG$.

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Sofia Brenner, Burkhard Külshammer. 2022-12-03. Group algebras in which the socle of the center is an ideal. https://arxiv.org/abs/2212.01601

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