论文标题
顶点对的独特性，$π$ - 分组
The uniqueness of vertex pairs in $π$-separable groups
论文作者
论文摘要
让$ g $是有限的$π$ - 可拆分的群体，其中$π$是一组素数，让$χ$是一个不可约的复杂性，是$π$的$π$ - $ g $的$π$。结果可能会以$ 2 \notinπ$失败。 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.
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.
