二极大子群为TI-子群的有限群的类保持Coleman自同构

设$H$是有限群$G$的一个子群，若对任意$g\in G$, $H\cap H^g=1$或者$H$,则称$H$为TI-子群. 设$G$是一个所有二极大子群为TI-子群的有限群，本文证明了$G$的每个类保持Coleman自同构是内自同构. 作为本结果的一个直接推论，得到了这样的群$G$有正规化子性质.

Class-Preserving Coleman Automorphisms of Finite Groups Whose Second Maximal Subgroups Are TI-Subgroups

Recall that a subgroup $H$ of a finite group $G$ is called a TI-subgroup if $H\cap H^{g}=1$ or $H$ for each $g\in G$. Suppose that $G$ is a finite group whose second maximal subgroups are TI-subgroups. It is shown that every class-preserving Coleman automorphism of $G$ is an inner automorphism. As an immediate consequence of this result, we obtain that the normalizer property holds for $G$.