OIST Representation Theory Seminar

Benjamin Sambale, Leibniz Universität Hannover

Title: 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.

Zoom info can be found on the seminar webpage.