Real ordinary characters and real Brauer characters

Tiep, Pham

doi:10.1090/S0002-9947-2014-06148-5

Real ordinary characters and real Brauer characters
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Trans. Amer. Math. Soc. 367 (2015), 1273-1312 Request permission

Abstract:

We prove that if $G$ is a finite group and $p$ is a prime such that the degree of every real-valued irreducible complex, respectively real-valued irreducible $p$-Brauer character, of $G$ is coprime to $p$, then $\mathbf {O}^{p’}(G)$ is solvable. This result is a generalization of the celebrated Ito–Michler theorem for real ordinary characters, respectively real Brauer characters, with Frobenius-Schur indicator $1$.

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