no. 1
Group algebras in which the socle of the center is an ideal
Brenner, Sofia1, 2; Külshammer, Burkhard2  
1 Department of Mathematics, TU Darmstadt, Germany
2 Institute for Mathematics, Friedrich Schiller University Jena, Germany
Annals of Representation Theory, Volume 1 (2024) no. 1, pp. 1-19.

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.

Received:
Accepted:
Published online:
DOI: 10.5802/art.1
Classification: 20C05, 20C20, 16S34

Brenner, Sofia 1, 2; Külshammer, Burkhard 2

1 Department of Mathematics, TU Darmstadt, Germany
2 Institute for Mathematics, Friedrich Schiller University Jena, Germany
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Brenner, Sofia; Külshammer, Burkhard. Group algebras in which the socle of the center is an ideal. Annals of Representation Theory, Volume 1 (2024) no. 1, pp. 1-19. doi : 10.5802/art.1. https://art.centre-mersenne.org/articles/10.5802/art.1/

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