The p-parts of character degrees in p-solvable groups

I. Martin (Irving) Isaacs

Vol. 36 (1971), No. 3, 677–691

DOI: 10.2140/pjm.1971.36.677

Abstract

Let G be a finite group and Irr(G) the set of irreducible complex characters of G. Fix a prime integer p and let e(G) be the largest integer such that p^e(G) divides χ(1) for some χ ∈ Irr(G). The purpose of this paper is to obtain information about the structure of G, and in particular about a Sylow p-subgroup of G, from a knowledge of e(G). If G is solvable, we obtain the bound 2e(G) + 1 for the derived length of an S_p subgroup of G. We also obtain some information about the normal structure of G in terms of e(G).

Mathematical Subject Classification 2000

Primary: 20C15

Milestones

Received: 6 October 1969

Published: 1 March 1971