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.
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