J Austral Math Soc Ser A 57 pp76--80, 1994.

Character Degrees and Nilpotence Class in p-Groups

Huai-Hui Chen and Xin-Hou Hua

Abstract

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 theorem 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 if the non-linear irreducible character degrees of G lie between p^a and p^b, where a £ b £ 2a - 2, then the nilpotence class of G is bounded by a function of p and b - a.

1991 AMS Subject Classification: 20C15

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Authors

Michael C. Slattery

Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee WI 53233, USA.