摘要
有限群G的子群H称为G的置换子群(或拟正规子群),如果H与G的任意子群K可置换(即HK=KH).设H,K和L都是群G的子群,且满足H≤K≤L,若H是K的拟正规子群,K是L的拟正规子群,必有H是L的拟正规子群,则称群G为PT-群.本文研究了群G的所有非正规极大子群M都是可解PT-群,得到群G为可解群的一个新的充分条件.
A subgroup H of a group G is called permutable（or quasinormal） if HK=KH for all subgroups K of G. A finite group G is called a PT-group if, for subgroups H, K and L satisfying H≤K≤L with H quasinormal in K and K quasinormal in L, it is always the case that H is quasinormal in L. In this paper, we investigated the always the case that H is quasinormal in L. In this paper, we investigated the influence of all non-normal maximal sub groups M of G being solvable PT-groups on solvablity of a finite group G. A new sufficient condition for a group G to be solvable was ziven.
出处
《海南师范大学学报（自然科学版）》
CAS
2015年第2期145-146,共2页
Journal of Hainan Normal University（Natural Science）
关键词
拟正规子群
PT-群
可解群
超可解群
quasinormal subgroups
PT-groups
solvable groups
supersolvable groups
