Embedding Properties Related to System Permutability

• 来源期刊: 代数集刊（英文版）
• 关键词: solvable Hall system subgroup permutability
• 年，卷（期）: 2002,（2）
• 页码范围: 155-161
• 页数: 7页
• 语种: 英文

摘要

A subgroup U of a finite solvable group G is system permutable in G if there is a Hall system ∑ of G such that US ≤ G for all S ∈∑. We introduce and investigate three properties, each apparently weaker than system permutability.We show that all three properties are equivalent to system permutability in a group of p-length at most 1 for each prime p, and they determine the same subgroup closed class as system permutability. We give an example to show that two of these properties are weaker than system permutability. For the third property,this is unresolved.