摘要
设G是一个有限群，P是｜G｜的一个素因子，P是G的一个Sylow／p-子群，A和B是G的两个子群．当P阶子群在G中共轭置换且可补时，获得了P的正规性并描述了P的结构．这表明当G的极小子群均在G中共轭置换且可补时，G是幂零的．特别地，当P是G的阶的最小素因子时，证明了G是p-可分解的．在此基础上，把上述结论推广到G=AB并且A∪B中的极小子群具有相应性质时的情形．除此之外，还证明了当C有一个循环极大子群是F（G）-共轭置换时G的超可解性．
Let G be a finite group, p be a prime factor of ｜G｜, A and B be two subgroups of G. We obtain the normality and the structure of P when the p order subgroups are conjugate permutable and complemented in G. It shows that G is nilpotent when the minimal sub- groups are conjugate permutable and complemented in G. Especially, when p is the minimal prime factor of the order of G, we prove that G is p-decomposable. Based on these, we gen- eralize the above conclusions under the condition that G = AB and the minimal subgroups contained in A ∪ B admit the corresponding properties. Besides, the supersolvability of G is obtained when G has a cyclic maximal subgroup which is F（G）-conjugate permutable.
作者
赵先鹤
陈瑞芳
ZHAO Xian-he;CHEN Rui-fang(College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China)
出处
《数学的实践与认识》
北大核心
2018年第20期184-188,共5页
Mathematics in Practice and Theory
基金
国家自然科学基金(11501176,U1504101,U1204101)
河南省高校青年骨干教师项目资助课题
关键词
共轭置换子群
幂零群
超可解群
极小子群
极大子群
conjugate-permutable subgroups
nilpotent groups
supersolvable groups
min-imal subgroups
maximal subgroups
