Lifting Brauer characters of p-solvable groups

I. Martin (Irving) Isaacs

Vol. 53 (1974), No. 1, 171–188

DOI: 10.2140/pjm.1974.53.171

Abstract

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 p≠2, 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

Milestones

Received: 23 July 1973

Revised: 10 October 1973

Published: 1 July 1974