Abstract Let G be a finite group and assume that a group of automorphisms A is acting on G such that A and G have coprime orders. Recall that a subgroup H of G is said to be a TI-subgroup if it has trivial intersection with its distinct conjugates in G. We study the solubility and other properties of G when we assume that certain invariant subgroups of G are TI-subgroups, precisely when all A-invariant subgroups, all non-nilpotent A-invariant subgroups, and all non-abelian A-invariant subgroups of G, respectively, are TI-subgroups.

中文翻译：

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不变的 TI 子群和有限群的结构

摘要 设 G 是一个有限群，并假设一组自同构 A 作用于 G，使得 A 和 G 具有互质阶。回想一下，如果 G 的子群 H 与 G 中的不同共轭具有平凡的交集，则称其为 TI 子群。 当我们假设 G 的某些不变子群是 TI 子群时，我们研究 G 的溶解度和其他性质，正是当 G 的所有 A 不变子群、所有非幂零 A 不变子群和 G 的所有非阿贝尔 A 不变子群分别是 TI 子群时。