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Character degree sets that do not bound the class of a -group

Authors:	I M Isaacs M C Slattery

Institution:	Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706 ; Department of Mathematics, Statistics and Computer Science, Marquette University, P.O. Box 1881, Milwaukee, Wisconsin 53201

Abstract:	Suppose that we are given a set $\mathcal{S}$ of powers of a prime and that $1 \in \mathcal{S}$ . A technique is presented that enables the construction of a -group of specified nilpotence class such that its set of irreducible character degrees is exactly $\mathcal{S}$ . If $\vert\mathcal{S}\vert \ge 2$ , then this can be done for $2 \le n \le p$ and if $p \in \mathcal{S}$ , then the only requirement is $2 \le n$ .

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