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Character degrees and nilpotence class in p-groups

Published online by Cambridge University Press:  09 April 2009

Michael C. Slattery
Michael C. Slattery
Affiliation:
Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee WI 53233, USA
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Abstract

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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 a ≤ b ≤ 2a − 2, then the nilpotence class of G is bounded by a function of p and b − a.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 57 , Issue 1 , August 1994 , pp. 76 - 80
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), 467–510.Google Scholar
[2]Slattery, M., ‘Character degrees and derived length in p-groups’, Glasgow Math J. 30 (1988), 221–230.CrossRefGoogle Scholar