Finite Groups with a System of Nilpotent Subgroups

• 来源期刊: 代数集刊（英文版）
• 关键词: finite group nilpotent subgroup solvable group
• 年，卷（期）: 2005,（2）
• 页码范围: 199-204
• 页数: 6页
• 语种: 英文

摘要

Let G be a finite group and p an odd prime. Let ψ*p(G) be the set of proper subgroups M of G with |G: M| not a prime power and |G: M|p = 1. In this paper,we investigate the structure of G if every member of ψ*p(G) is nilpotent. In particular, a new characterization of PSL(2, 7) is obtained. The proof of the theorem depends on the classification of finite simple groups.