On p-parts of character degrees

Let G be a finite group and p be a prime. In this paper, we get the sharp bound for |G/Op(G)|p under the assumption that either p 2 ∤ χ(1) for all χ ∈ Irr(G) or p2 ∤ φ(1) for all φ ∈ IBrp(G). This would settle two conjectures raised by Lewis, Navarro, Tiep, and Tong-Viet in [7].

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