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

Isaacs, I.; Slattery, M.

doi:10.1090/S0002-9939-02-06364-5

Character degree sets that do not bound the class of a $p$-group
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by I. M. Isaacs and M. C. Slattery PDF

Proc. Amer. Math. Soc. 130 (2002), 2553-2558 Request permission

Abstract:

Suppose that we are given a set $\mathcal {S}$ of powers of a prime $p$ and that $1 \in \mathcal {S}$. A technique is presented that enables the construction of a $p$-group of specified nilpotence class $n$ such that its set of irreducible character degrees is exactly $\mathcal {S}$. If $|\mathcal {S}| \ge 2$, 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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