Zeros of $S$-characters

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Breuer, Thomas, Joswig, Michael, Malle, Gunter
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866917497403342848
author Breuer, Thomas
Joswig, Michael
Malle, Gunter
author_facet Breuer, Thomas
Joswig, Michael
Malle, Gunter
contents 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 present examples that this does not generalise to $S$-characters, thereby answering a question posed by J-P. Serre.
format Preprint
id arxiv_https___arxiv_org_abs_2408_16785
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Zeros of $S$-characters
Breuer, Thomas
Joswig, Michael
Malle, Gunter
Group Theory
Representation Theory
20C15, 20D08, 20B05, 11P21, 52B20
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 present examples that this does not generalise to $S$-characters, thereby answering a question posed by J-P. Serre.
title Zeros of $S$-characters
topic Group Theory
Representation Theory
20C15, 20D08, 20B05, 11P21, 52B20
url https://arxiv.org/abs/2408.16785