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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^{1, 2}; Külshammer, Burkhard

^{2}

@article{ART_2024__1_1_1_0, author = {Brenner, Sofia and K\"ulshammer, Burkhard}, title = {Group algebras in which the socle of the center is an ideal}, journal = {Annals of Representation Theory}, pages = {1--19}, publisher = {The Publishers of ART}, volume = {1}, number = {1}, year = {2024}, doi = {10.5802/art.1}, language = {en}, url = {https://art.centre-mersenne.org/articles/10.5802/art.1/} }

TY - JOUR AU - Brenner, Sofia AU - Külshammer, Burkhard TI - Group algebras in which the socle of the center is an ideal JO - Annals of Representation Theory PY - 2024 SP - 1 EP - 19 VL - 1 IS - 1 PB - The Publishers of ART UR - https://art.centre-mersenne.org/articles/10.5802/art.1/ DO - 10.5802/art.1 LA - en ID - ART_2024__1_1_1_0 ER -

%0 Journal Article %A Brenner, Sofia %A Külshammer, Burkhard %T Group algebras in which the socle of the center is an ideal %J Annals of Representation Theory %D 2024 %P 1-19 %V 1 %N 1 %I The Publishers of ART %U https://art.centre-mersenne.org/articles/10.5802/art.1/ %R 10.5802/art.1 %G en %F ART_2024__1_1_1_0

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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