Finite Non-abelian Simple Groups Which Contain a Non-trivial Semipermutable Subgroup

• 来源期刊: 代数集刊（英文版）
• 关键词: simple groups semipermutable subgroups s-semipermutable
• 年，卷（期）: 2005,（2）
• 页码范围: 301-307
• 页数: 7页
• 语种: 英文

摘要

A subgroup H of a group G is called semipermutable if it is permutable with every subgroup K of G with (|H|, |K|) = 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with (p, |H|) = 1. In this paper, we classify all finite non-abelian simple groups which contain a non-trivial semipermutable (s-semipermutable)subgroup. As a corollary of our main result, we give a complete answer to an unsolved problem in group theory proposed by V.S. Monakhov in 1990.