AI 中文总结
该研究针对有限群主块的Eaton-Moretó猜想，通过构造主p-块中满足次数条件的不可约特征标，结合Dade射影猜想证明了该猜想成立。
AI 中文摘要
设G为有限群，p为素数，若P是G的非阿贝尔Sylow p-子群，m(P)是P的最小非线性不可约特征标次数，我们证明存在G主p-块中的不可约特征标χ，满足1<χ(1)_p≤m(P)，给出主块Eaton-Moretó猜想的一个不等式；在假设Dade射影猜想成立的前提下，这一结果可推出主块的Eaton-Moretó猜想成立。
英文摘要
Let $G$ be a finite group and let $p$ be a prime. If $P$ is a nonabelian Sylow $p$-subgroup of $G$ and $m(P)$ is the smallest non-linear irreducible character degree of $P$, we prove that there exists $χ\in {\rm Irr}(G)$ in the principal $p$-block of $G$ such that $1<χ(1)_p\le m(P)$, giving one inequality of the Eaton-Moretó conjecture for principal blocks. This, assuming Dade's Projective conjecture, implies the Eaton-Moretó conjecture for principal blocks.
