Let G be a finite group, and $\mathrm{T}(G)$ be the sum of all complex irreducible character degrees of G. In this paper, we aim to characterize the structure of finite groups in terms of $\mathrm{T}(G)$. We show that if $|G|/\mathrm{T}(G)<(p+1)/2$, then G has a normal Sylow p-subgroup; and that if $|G|/\mathrm{T}(G)<3p^2/(p^2+2)$, then G is p-supersolvable, where p is a prime.

中文翻译：

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字符度数总和的两个结果

令G为有限群，且$\mathrm{吨}(G)$是G的所有复数不可约字符度的总和。在本文中，我们的目标是刻画有限群的结构$\mathrm{吨}(G)$. 我们证明如果$|G|/\mathrm{吨}(G)<(磷+1)/2$，则G有一个正规 Sylow p -子群；如果$|G|/\mathrm{吨}(G)<3{磷}^2/({磷}^2+2)$，则G是p超可解的，其中p是素数。