Zeros of S -characters

Journal of Computational Algebra, vol. 13-14, pp. 100031

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. J-P. Serre asked whether this generalises to S -characters. We provide a translation of this question into the language of polyhedral geometry and thereby construct many counterexamples, using the capabilities of the computer algebra system OSCAR .

Authors 3

1. Thomas Georg Karl Breuer corresponding Aachen Lehrstuhl für Algebra und Zahlentheorie

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl für Algebra und Zahlentheorie, RWTH Aachen University, Pontdriesch 14/16, 52062 Aachen, Germany

2. Michael Joswig

   Technische Universität Berlin

   Affiliation as printed

   Chair of Discrete Mathematics/Geometry, Technische Universität Berlin, Germany

3. Gunter Malle

   Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau

   Affiliation as printed

   FB Mathematik, RPTU, Postfach 3049, 67653 Kaiserslautern, Germany