Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-22T06:43:28.194Z Has data issue: false hasContentIssue false

Character degrees and nilpotence class in p-groups

Published online by Cambridge University Press:  09 April 2009

Michael C. Slattery
Affiliation:
Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee WI 53233, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Work of Isaacs and Passman shows that for some sets X of integers, p-groups whose set of irreducible character degrees is precisely X have bounded nilpotence class, while for other choices of X, the nilpotence class is unbounded. This paper presents a theoren which shows some additional sets of character degrees which bound nilpotence class within the family of metabelian p-groups. In particular, it is shown that is the non-linear irreducible character degrees of G lie between pa and pb, where ab ≤ 2a − 2, then the nilpotence class of G is bounded by a function of p and b − a.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Isaacs, M. and Passman, D., ‘A characterization of groups in terms of the degrees of their character II’, Pacific J. Math. 24 (1968), 467510.Google Scholar
[2]Slattery, M., ‘Character degrees and derived length in p-groups’, Glasgow Math J. 30 (1988), 221230.CrossRefGoogle Scholar