Minimal splitting fields for group representations. II

Burton I. Fein

Vol. 77 (1978), No. 2, 445–449

DOI: 10.2140/pjm.1978.77.445

Abstract

Let p be an arbitrary prime and m an arbitrary positive integer. A finite group G is constructed which has an irreducible complex representation T with character χ such that the Schur index of χ over Q is p but the minimum of [K : Q(χ)], taken over all abelian extensions K of Q in which T is realizable, is p^m.

Mathematical Subject Classification 2000

Primary: 20C15

Secondary: 12A57

Milestones

Received: 23 September 1975

Published: 1 August 1978