Rational Groups and a Characterization of a Class of Permutation Groups

2019/05/17 by Cecil Andrew Ellard, Ellard, Cecil Andrew · 2 citations
Mathematics · Computer Science · Engineering · #Finite Group Theory Research #Coding theory and cryptography #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1905.07431

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

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

Related

• Rational conjugacy classes and rational characters for some finite simple groups
• A Geometric Characterization of Rational Groups
• On groups with at most five irrational conjugacy classes
• On Semi-Rational Groups
• A characterization of finite groups by certain Galois conjugacy class of irreducible characters