Let $G$ be a finite group and $p$ be an odd prime. We show that if $\mathbf{O}_{p}(G)=1$ and $p^{2}$ does not divide every irreducible $p$-Brauer character degree of $G$, then $|G|_{p}$ is bounded by $p^{3}$ when $p\geqslant 5$ or $p=3$ and $\mathsf{A}_{7}$ is not involved in $G$, and by $3^{4}$ if $p=3$ and $\mathsf{A}_{7}$ is involved in $G$.

中文翻译：

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关于部分 BRAUER 字符度数的注释

让$G$是一个有限群并且$p$是一个奇数素数。我们证明如果$\mathbf{O}_{p}(G)=1$和$p^{2}$不划分每一个不可约$p$-Brauer 性格程度$G$， 然后$|G|_{p}$由$p^{3}$什么时候$p\geqslant 5$要么$p=3$和$\mathsf{A}_{7}$不参与$G$，并由$3^{4}$如果$p=3$和$\mathsf{A}_{7}$参与$G$.