Rational Groups and a Characterization of a Class of Permutation Groups

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.

Cited by in corpus (2)

• The Sym(3) Conjecture and Alt(8)
• A Geometric Characterization of Rational Groups