Groups with few 𝑝’-character degrees in the principal block

Giannelli, Eugenio; Rizo, Noelia; Sambale, Benjamin; Schaeffer Fry, A.

doi:10.1090/proc/15143

Groups with few $p’$-character degrees in the principal block
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by Eugenio Giannelli, Noelia Rizo, Benjamin Sambale and A. A. Schaeffer Fry PDF

Proc. Amer. Math. Soc. 148 (2020), 4597-4614 Request permission

Abstract:

Let $p\ge 5$ be a prime and let $G$ be a finite group. We prove that $G$ is $p$-solvable of $p$-length at most $2$ if there are at most two distinct $p’$-character degrees in the principal $p$-block of $G$. This generalizes a theorem of Isaacs–Smith as well as a recent result of three of the present authors.

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