Characters, Commutators and Centers of Sylow Subgroups
arXiv:2204.04407
Abstract
The character table of a finite group G determines whether |P:P'|=p^2 and whether |P: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.
18 pages, referee's comments incorporated