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}
}