幂零群的若干充分条件

本文利用Ｃ－正规子群的性质，得到了若干有限群为幂零群的充分条件，推广了一些著名定理，如Ｔｈｏｍｐｓｏｎ定理及Ｉｔ＾ｏ定理。     

有限群的某些定理

本文给出了有限群的如下结果：１）成为可解群与超可解群的条件；２）推广了Ｉｔｏ定理，３）超可解且内幂零的群结构。     

某些子群是半正规的有限群

本文旨在考查极大子群对有限群结构的影响．首先给出了商群超可解的群是超可解群的若干充分条件；其次考查了ｎ－极大子群对有限群的可解性及超可解性的影响     

关于可解群的若干充分条件

本文在［１］的基础上，利用半正规子群的概念考查了有限群的可解性，得到了若干充分条件．     

On the Supersolvability of QCLT-Groups

ＯｎｔｈｅＳｕｐｅｒｓｏｌｖａｂｉｌｉｔｙｏｆＱＣＬＴ－ＧｒｏｕｐｓＷａｎｇＰｉｎｃｈａｏ（王品超）；ＬｕＺａｉｐｉｎｇ（路在平）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＱｕｆｕＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｑｕｆｕ，Ｓｈａｎｄｏｎｇ，...     

关于有限群两个超可解子群之积的问题

In this paper, we give some sufficient conditions for products of two supersolvable sub-groups to be supersolvable groups. Our results generalize some known results.Theorem 1 Let G = HK,(|H|,|K|) = 1, Where H and K are two supersolvable sub-groups. If H is commutative with every maximal subgroup of K, and K is commutative with every maximal subgroup of H, then G is supersolvable.Theorem 2 Let G = HK, H ∩ K = 1, H G, and K be quasinormal in H. If H, K are supersolvable, the G is supersolvable.Theorem 3 Let G= HK,(|H|,|K|) = 1,H,K be two supersolvable subgroups. If H is commutative with any Sylow subgroup of K and any maximal subgroup of every sylow subgroup of K, and K is commutative with any sylow subgroup of H and any maximal subgroup of every sylow subgroup of H, then G is supersolvable. Theorem 4 If H,K are two supersolvable subgroups of G, G= HK, G′is nilpotent, H is quasi normal K, and K is quasi normal in H,then G is supersolvable. Theorem 5 If H,K are two supersolvable subgroups of G, G= HK, H′? G,[H,K]? G,[H,K] is nilpotent, H is quasi normal in K, and K is quasi normal in H,then G is supersolvable.     

中心为单位元的一个无限p-群

无限 p-群当具有异于单位元 E 的有限共轭元素系时,则该群的中心异于 E,但也存在无限 p-群,它的中心即为单位元.Kypo(?)等都给出过例子,但较为繁琐,现这里给出一例.设