A Note on TI-Subgroups of a Finite Group

• 作者: Cui Zhang Jiangtao Shi
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 幂零子群 有限群 注记 OFG 幂零群
• 年，卷（期）: 2014,（2）
• 页码范围: 343-346
• 页数: 4页
• 分类号: O152.1
• 语种: 中文

摘要

Let G be a finite group and H a subgroup of G. Recall that H is said to be aTI-subgroup ofG ifHg∩H = 1 or H for each b∈ G. In this note, we prove that if all non-nilpotent subgroups of a finite non-nilpotent group G are TI-subgroups, then G is soluble, and all non-nilpotent subgroups of G are normal.