Vol. 36, No. 3, 1971

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 325: 1
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
The p-parts of character degrees in p-solvable groups

I. Martin (Irving) Isaacs

Vol. 36 (1971), No. 3, 677–691
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 pe(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 Sp 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
Authors
I. Martin (Irving) Isaacs