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arXiv · 2102.09165

On p-parts of character degrees

Guohua Qian·Yong Yang
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Abstract

In this paper, we get the sharp bound for $|G/O_p(G)|_p$ under the assumption that either $p^2 \nmid \chi(1)$ for all $\chi \in {\rm Irr}(G)$ or $p^2 \nmid \phi(1)$ for all $\phi \in {\rm IBr}_p(G)$. This would settle two conjectures raised by Lewis, Navarro, Tiep, and Tong-Viet.

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Guohua Qian, Yong Yang. 2021-02-18. On p-parts of character degrees. https://arxiv.org/abs/2102.09165

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