两个σ-超可解子群的积

The product of two σ-supersoluble groups

摘要: 设Nσ是指所有σ-幂零群所有构成的群类，并记GNσ是G的σ-幂零群上根.我们称群G是σ-超可解的，如果G的含于GNσ的主因子是循环的.群G的子群H称为与子群T是完全c-置换的，如果存在元素x∈〈H,T〉满足HTx= TxH.利用子群的完全c-置换性研究两个σ-超可解群的积所构成的有限群的结构.

Abstract: Let Nσ denote the classes of all σ-nilpotent groups and GNσ be the σ-nilpotent residual of G. We say that G is σ-supersoluble if each chief factor of G below GNσ is cyclic. A subgroup H of G is said to be completely c-permutable with a subgroup T of G if there exists an element x∈〈H,T〉 such that HTx=TxH.