弱c-正规与有限群的可解性

journal6 ›› 2008, Vol. 29 ›› Issue (3): 29-30.

弱c-正规与有限群的可解性

(1.广西大学数学与信息科学学院,广西南宁 530004；2.湖南科技学院，湖南永州 425100)

出版日期:2008-05-25 发布日期:2012-05-23
作者简介:吴建平（1981-），男，湖南永州人，硕士，主要从事有限群研究.

Weakly c-Normal Subgroups and Solvability of Finite Groups

(1.School of Mathematics and Information Sciences，Guangxi University,Nanning 530004,Guangxi China;2.Hunan University of Science and Engineering,Yongzhou 425100,Hunan China)

Online:2008-05-25 Published:2012-05-23

摘要/Abstract

摘要：群G的一个子群H称为在G中弱c-正规，如果存在G的一个次正规子群K，使得G=HK且H∩K≤HG，其中HG=∩x∈GHx是包含在H中的G的极大正规子群．利用子群的弱c-正规性来探索一个群为可解群.

关键词： 极大子群, 弱c-正规子群, 可解群

Abstract: A subgroup H of a finite group G is said to be weakly c-normal in G;if there exists a subnormal subgroup K of G such that G=HK and H∩K≤HG=CoreG(H),where HG=∩x∈GHx is the　largest normal subgroup of G,contained in H.Some conditions of a solvable group are given by using weakly　c-normality of subgroups.

Key words: maximal group, weakly c-normal subgroup, solvable group

吴建平, 基艳. 弱c-正规与有限群的可解性[J]. journal6, 2008, 29(3): 29-30.

WU Jian-Ping, JI Yan. Weakly c-Normal Subgroups and Solvability of Finite Groups[J]. journal6, 2008, 29(3): 29-30.

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