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Journal of the London Mathematical Society Advance Access originally published online on November 14, 2007
Journal of the London Mathematical Society 2007 76(3):667-682; doi:10.1112/jlms/jdm082
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© 2007 London Mathematical Society

Nondivisibility among character degrees II: Nonsolvable groups

Gunter Malle

Fachbereich Mathematik
Universität Kaiserslautern
Postfach 3049
D-67653 Kaiserslautern
Germany

Alexander Moretó

Departament d’Àlgebra
Universitat de València
46100 Burjassot
València
Spain
Alexander.Moreto{at}uv.es

We say that a finite group G is an NDAD-group (no divisibility among degrees) if for any 1 < a < b in the set of degrees of the complex irreducible characters of G, a does not divide b. In this article, we determine the nonsolvable NDAD-groups. Together with the work of Lewis, Moretó and Wolf (J. Group Theory 8 (2005)), this settles a problem raised by Berkovich and Zhmud’, which asks for a classification of the NDAD-groups.

2000 Mathematics Subject Classification 20C15 (primary), 20C33 (secondary).

Received April 6, 2006; revised December 7, 2006; published online November 14, 2007.


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