有限群为超可解群的充要条件  

THE NECESSARY AND SUFFICIENT CONDITIONS FOR A FINITE GROUP TO BE SUPERSOLVABLE

作　　者：郭秀云[1] 

机构地区：[1]山西大学

出　　处：《数学杂志》1989年第2期161-164,共4页Journal of Mathematics

摘　　要：用置换条件刻画有限可解群的超可解性已有大量结果,本文的目的是给出另外一些有限可解群为超可解的充要条件。其主要结果是: 1.设G是满足置换条件的有限可解群,则G是超可解群当且仅当如下条件之一成立。 1)G的2-Sylow子群G_2的换位子群G_2′G. 2)G有正规2-补。 2.设G是有限可解群,则G超可解当且仅当G和G′均满足置换条件.There have been many results to characterise supersolublity of finite solvable groups by permutizer condition. The purpose of this paper is to prove another necessary and sufficient conditions for a finite solvable group to be supersolvable. The main results are the following:1. Let G be a finite solvable group satisfied permutizer condition, then G is a supersolvable group if and only if one of the following conditions is true.1) Derived group G_2' of G_2 is normal of G where G_2∈S_yl_2(G).2) There is a normal 2-complement in G.2. Let G be a finite solvable group, then G is a supersolvable group if and only if G and G' satisfie permutizer condition.

关 键 词：有限群 超可解群 置换条件 

分 类 号：O152.1[理学—数学]