Vol. 23, No. 2, 1967

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 297: 1
Vol. 296: 1  2
Vol. 295: 1  2
Vol. 294: 1  2
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Finite groups with small character degrees and large prime divisors

I. Martin (Irving) Isaacs

Vol. 23 (1967), No. 2, 273–280
Abstract

In earlier papers of this author and D. S. Passman, some properties of finite groups with r.b.n were discussed, where we say that a group G has r.b. n (representation bound n) if all the absolutely irreducible characters of G have degree n. In the present paper, the situation where p||G| is a prime which in some sense is large when compared with n is explored. An earlier result of this nature to which we refer states that if G has r.b. (p 1) then an Sp subgroup of G is normal and abelian. Here we get a weak result of this general type for groups with r.b. (p2 p 1). For smaller representation bounds, more information can be obtained. Our main result is:

THEOREM. Let G have r.b. (2p 8) for a prime p. Then either

(i) An Sp of G is normal and abelian,

(ii) G is solvable and has p-length 1 or

(iii) G = P ×H where P is an abelian p-group and p2 ↑|H|.

Mathematical Subject Classification
Primary: 20.25
Milestones
Received: 25 March 1966
Published: 1 November 1967
Authors
I. Martin (Irving) Isaacs