AI 中文总结
研究有限群\(G\)主\(p -\)块特征标，通过设\(\pi = \{2, q\}\)，证明主\(p -\)块含特定非平凡不可约特征标，给出了相关结果的主块版本。
AI 中文摘要
设\(\pi = \{2, q\}\)，其中\(q\)为奇素数。设\(G\)为阶数能被\(\pi\)中素数\(p\)整除的有限群。我们证明\(G\)的主\(p\)-块包含一个非平凡不可约特征标，其度数不能被\(2\)或\(q\)整除，且取值域包含在\(q\)次分圆扩张中。此陈述同时给出了Navarro - Tiep和Giannelli - Hung - Schaeffer Fry - Vallejo结果的主块版本。
英文摘要
Let $π=\{ 2, q \}$ where $q$ is an odd prime. Let $G$ be a finite group of order divisible by a prime $p \in π$. We show that the principal $p$-block of $G$ contains a nontrivial irreducible character of degree not divisible by $2$ nor $q$ and with field of values contained in the $q$th cyclotomic extension. This statement simultaneously provides a principal block version of results of Navarro--Tiep and Giannelli--Hung--Schaeffer Fry--Vallejo.
