$π$ -可分群顶点对的唯一性
The uniqueness of vertex pairs in $π$-separable groups
摘要：
设$G$是一个有限的$π$ -可分群，其中$π$是素数的集合，$χ$是一个不可约复特征标，它是$G$的某个$π$ -部分特征标的$π$ -提升. Cossey和Lewis证明了如果$2\inπ$，则$χ$的所有顶点对在$G$中都是线性共轭的，但对于$2\notinπ$，这一结果可能失败.本文在$2\notinπ$情形下引入扭顶点的概念，并在$χ$是$G$的$π$ -链$\mathcal N$的$\mathcal N$ -提升或有线性Navarro顶点的条件下，建立了线性扭顶点的唯一性，从而回答了他们提出的一个问题.
英文摘要：
Let $G$ be a finite $π$-separable group, where $π$ is a set of primes, and let $χ$ be an irreducible complex character that is a $π$-lift of some $π$-partial character of $G$.It was proved by Cossey and Lewis that all of the vertex pairs for $χ$ are linear and conjugate in $G$ if $2\inπ$, but the result can fail for $2\notinπ$. In this paper we introduce the notion of the twisted vertices in the case where $2\notinπ$, and establish the uniqueness for linear twisted vertices under the conditions that either $χ$ is an $\mathcal N$-lift for a $π$-chain $\mathcal N$ of $G$ or it has a linear Navarro vertex, thus answering a question proposed by them.
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