Groups of p-central type

Abstract: A finite group \(G\) with center \(Z\) is of central type if there exists an irreducible character \(\chi\) such that \(\chi(1)^2=|G:Z|\). Howlett–Isaacs have shown that such groups are solvable. A corresponding theorem for \(p\)-Brauer characters was proved by Navarro–Späth–Tiep under the assumption that \(p\ne 5\). I have shown that there are no exceptions for \(p=5\). Moreover, I give some applications to \(p\)-blocks with a unique Brauer character.

combinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

OIST representation theory seminar

Series comments: Timings of this seminar may vary from week to week.