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

2022/12/03 by Sofia Brenner, Brenner, Sofia, Burkhard Külshammer +1
Mathematics · #16S34 (Secondary) #20C05 (Primary) 20C20 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2212.01601

openalex publication_date 2022/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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