Seminar

Group Theory Seminar

Detecting blocks from the character table

Speaker:  Benjamin Sambale (Leibniz University Hannover)
Date:  Thursday, 10 February 2022 - 11:30
Place:  Aula Naranja, ICMAT

Abstract:

Many properties of a finite group \(G\) can be detected from its complex character table \(X(G) \). We are particularly interested in local properties, i.e. data related to a Sylow \(p\)-subgroup \(P\) of \(G\). It has been shown that \(X(G) \) determines whether \(P\) is abelian and in that case the isomorphism type of \(P\) is determined as well. In this work we replace \(P\) by a defect group of a block of \(G\) and show (among other things) that the exponent of the center $\exp(\Z(D))$ is determined by \(X(G) \).