弱ST-群的一个充要条件(英文)  

A Necessary and Sufficient Condition for Weakly ST-Groups

作　　者：郭鹏飞[1] 韩章家[2] 石化国[3] 

机构地区：[1]连云港师范高等专科学校数学系,江苏连云港222006 [2]成都信息工程学院数学学院,四川成都610225 [3]四川职业技术学院应用数学与经济系,四川遂宁629000

出　　处：《四川师范大学学报（自然科学版）》2012年第5期628-631,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：supported by National Science Foundation of China(11001226);Youth Foundation of Department of Education of Sichuan Province(11ZB174);Special Foundation from Department of Land and Resources of Shanxi Province(2009SXGTKY06);supported by Research Fund of Chengdu University of Information Technology(KYTZ201003);Qing Lan Project of Jiangsu Province~~

摘　　要：研究有限群的广义正规子群性质的传递性一直是有限群论重要的课题之一,而且获得了许多有意义的研究结果.若群G中s-置换性具有传递关系,则称G为PST-群.若群G的子群H与G的满足条件(p,|H|)=1的每个Sylow p-子群可置换,则称H在G中s-半正规.称群G为弱ST-群,若G的每个次正规子群都在G中s-半正规.给出有限群G为可解弱ST-群当且仅当G为可解PST-群,并且证明了在有限可解群中可解弱ST-性质是子群遗传的.The transitivity of some kind of generalized normality of subgroups has been studied in finite group theory and many meaningful results are obtained. A group G is called a PST-group if s-permutability is transitive in G. A subgroup H of a group G is said to be s-seminormal if H permutes with every Sylow p-subgroup of G with （p, │H│ ） = 1. In this paper, we call a group C a weakly ST-group if every subnormal subgroup of C is s-seminormal in G. We show that a finite group G is a solvable weakly ST-group if and only if G is a solvable PST-group, and if G is a solvable weakly ST-group, then all subgroups of G are also solvable weakly ST-groups.

关 键 词：弱ST-群 PST-群 ST-群 超可解群 

分 类 号：O152.1[理学—数学]