Primitive characters of odd order groups

Claudio Marchi

Primitive characters of odd order groups

Group Theory 2019-06-27 v1 Representation Theory

Authors: Claudio Marchi

Abstract

Let $G$ be a finite group of odd order. We show that if $\chi$ is an irreducible primitive character of $G$ then for all primes $p$ dividing the order of $G$ there is a conjugacy class such that the $p-$ part of $\chi(1)$ divides the size of that conjugacy class. We also show that for some classes of groups the entire degree of an irreducible primitive character $\chi$ divides the size of a conjugacy class.

Keywords

character theory character theory of finite groups finite groups

Cite

@article{arxiv.1906.11207,
  title  = {Primitive characters of odd order groups},
  author = {Claudio Marchi},
  journal= {arXiv preprint arXiv:1906.11207},
  year   = {2019}
}

Comments

10 pages

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