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On p-parts of character degrees

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 نشر من قبل Yong Yang
 تاريخ النشر 2021
  مجال البحث
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In this paper, we get the sharp bound for $|G/O_p(G)|_p$ under the assumption that either $p^2 mid chi(1)$ for all $chi in {rm Irr}(G)$ or $p^2 mid phi(1)$ 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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