Speaker: Gunter Malle and Thomas Breuer (Kaiserslautern, Aachen)
Title: Zeros of \(S\)-Characters
Abstract:
The concept of \(S\)-characters of finite groups was introduced by Zhmud as a generalisation of transitive permutation characters. Any non-trivial \(S\)-character takes a zero value on some group element. By a deep result depending on the classification of finite simple groups a non-trivial transitive permutation character even vanishes on some element of prime power order. We study this property for \(S\)-characters, in particular answering a question posed by J.-P. Serre.