Speaker: Caroline Lassueur (Kaiserslautern)

Title: On Character Theory for Endo-Trivial Modules

Abstract:

Let $$k$$ be an algebraically closed field of characteristic $$p > 0$$ and $$G$$ be a finite group of order divisible by $$p$$. The aim of this talk is to describe a character-theoretic criterion to detect $$p$$-permutation endo-trivial $$kG$$-modules. When enough information is known about the character table of a group and that of the normaliser of a Sylow $$p$$-subgroup this criterion allows us to recover the full structure of the group of endo-trivial modules. Application to the sporadic groups, the Schur covers of the symmetric and alternating groups, or groups with Klein-four Sylow 2-subgroups will be discussed.