Characters, commutators and centers of Sylow subgroups

Navarro, Gabriel; Sambale, Benjamin

doi:10.1090/ert/653

Characters, commutators and centers of Sylow subgroups
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by Gabriel Navarro and Benjamin Sambale;

Represent. Theory 27 (2023), 717-733

DOI: https://doi.org/10.1090/ert/653

Published electronically: July 27, 2023

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Abstract:

The character table of a finite group $G$ determines whether $|P:P’|=p^2$ and whether $|P:\mathbf {Z}(P)|=p^2$, where $P$ is a Sylow $p$-subgroup of $G$. To prove the latter, we give a detailed classification of those groups in terms of the generalized Fitting subgroup.

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