Vol. 53, No. 1, 1974

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Lifting Brauer characters of p-solvable groups

I. Martin (Irving) Isaacs

Vol. 53 (1974), No. 1, 171–188

Let φ be an irreducible Brauer character for the prime p of the finite p-solvable group, G. By the Fong-Swan theorem, there exists an ordinary character, χ, which agrees with φ on p-regular elements. This cfiaracter is not, in general unique. It is proved here that χ can be chosen to be p-rational, i.e. its values lie in a field of the form Q[𝜖] with 𝜖n = 1 and p n. If p2, the character so chosen is unique and every irreducible constituent of its restriction to a normal subgroup is also p-rational and is modularly irreducible.

Mathematical Subject Classification 2000
Primary: 20C20
Received: 23 July 1973
Revised: 10 October 1973
Published: 1 July 1974
I. Martin (Irving) Isaacs