English

Rational Groups and a Characterization of a Class of Permutation Groups

Group Theory 2019-05-21 v1

Abstract

We prove that a finite group is rational if and only if it has a set of permutation characters which separate conjugacy classes. It follows from this that a finite group is rational if and only if it has a representation as a permutation group in which any two elements fixing the same number of letters are conjugate.

Keywords

Cite

@article{arxiv.1905.07431,
  title  = {Rational Groups and a Characterization of a Class of Permutation Groups},
  author = {Cecil Andrew Ellard},
  journal= {arXiv preprint arXiv:1905.07431},
  year   = {2019}
}