The Real Part of the Character Table of a Finite Group

Abstract

In the ordinary character table of a finite group G, the values of the real valued irreducible characters on the real conjugacy classes form a sub-table which is square by Brauer's permutation lemma. We call this table the real part of the character table of G. Unlike the ordinary character table, viewed as a square matrix the real part of the character table is often singular. We present some results linking nonsingularity of this table to other properties of G.

Key Words:

• Brauer permutation lemma
• Character table
• Real character

2000 Mathematics Subject Classification:

• Primary 20C15
• Secondary 15A03, 15A36

Notes

Communicated by A. Turull.