Gradewise Properties of Subgroups and Their Applications

• 来源期刊: 代数集刊（英文版）
• 关键词: finite group subgroup functor subgroup bifunctor gradewise property
• 年，卷（期）: 2017,（2）
• 页码范围: 255-266
• 页数: 12页
• 语种: 英文
• DOI: 10.1142/S1005386717000141

摘要

For each finite group E,let (O)(E) be a binary relation on the set of all subgroups of E.If A and B are subgroups of a finite group G,then we say that the pair (A,B) enjoys the gradewise property (resp.,generalized gradewise property) (O) in G if G has a normal series F:1 =G0 ≤ G1 ≤.… ≤ Gt =G such that for each i =1,t,we have ((A ∩ Gi)Gi-1/Gi-1,BCi-1/Gi-1) ∈ (O)(G/Gi-1) (resp.,we have ((A∩Gi)Gi-1/Gi-1,(B∩Gi)Gi-1/Gi-1) ∈ (O)(G/Gi-1)).Using these concepts,we obtain some new characterizations for solubility and supersolubility of finite groups and generalize some known results.