Groups Whose Nonlinear Irreducible p-Brauer Characters are Real Valued

Abstract

Let p be a given prime. A finite group G whose all nonlinear irreducible p-Brauer characters are real valued is called a p-regular ℝ₁-group. The aim of this article is to show some results about the structures of p-regular ℝ₁-groups. In particular, we will build the connections between p-regular ℝ₁-groups and p-modular Frobenius groups. If these results apply to a finite group G with p∤|G|, we obtain similar results about finite groups whose nonlinear irreducible characters are real valued, and establish connections between these groups and Frobenius groups.

Key Words:

• p-Brauer character
• p-modular Frobenius group
• p-regular ℝ-group
• p-regular ℝ₁-group

2010 Mathematics Subject Classification:

• Primary: 20C15, 20C20

ACKNOWLEDGMENT

Authors appreciate greatly the referee for his careful reading of this paper and valuable comments on this paper.

Notes

Communicated by J. Zhang.