English

Rational representations and permutation representations of finite groups

Representation Theory 2016-01-29 v2 Group Theory

Abstract

We investigate the question which Q-valued characters and characters of Q-representations of finite groups are Z-linear combinations of permutation characters. This question is known to reduce to that for quasi-elementary groups, and we give a solution in that case. As one of the applications, we exhibit a family of simple groups with rational representations whose smallest multiple that is a permutation representation can be arbitrarily large.

Keywords

Cite

@article{arxiv.1405.6616,
  title  = {Rational representations and permutation representations of finite groups},
  author = {Alex Bartel and Tim Dokchitser},
  journal= {arXiv preprint arXiv:1405.6616},
  year   = {2016}
}

Comments

16 pages; minor improvements and corrections. To appear in Math. Ann

R2 v1 2026-06-22T04:23:25.893Z