论文标题
$ p $ - 理性的连续性和有限群体的$ p'$学位字符的下限
The continuity of $p$-rationality and a lower bound for $p'$-degree characters of finite groups
论文作者
论文摘要
令$ p $为PRIME，有限组为$ G $。我们建议在$ g $ $ g $的$ p'$ degr不可约字符的数量上，在$ g $ $ g $的换向器因子组方面。该界限是由于最近在角色值字段上的Navarro和Tiep [NT21]的猜想以及一种称为$ p $ - 理性的连续性的现象为$ p'$ - 度 - 度 - $ - 度 - 度。著名的McKay-Navarro猜想[NAV04]预测了这种连续性。我们以$ p = 2 $实现了界限和连续性属性。
Let $p$ be a prime and $G$ a finite group. We propose a strong bound for the number of $p'$-degree irreducible characters of $G$ in terms of the commutator factor group of a Sylow $p$-subgroup of $G$. The bound arises from a recent conjecture of Navarro and Tiep [NT21] on fields of character values and a phenomenon called the continuity of $p$-rationality level of $p'$-degree characters. This continuity property in turn is predicted by the celebrated McKay-Navarro conjecture [Nav04]. We achieve both the bound and the continuity property for $p=2$.
