有限核(2)-群  

Finite Core(2)-groups

作　　者：薛海波[1] 吕恒[2] 

机构地区：[1]重庆人文科技学院机电与信息工程学院,重庆401524 [2]西南大学数学与统计学院,重庆400715

出　　处：《重庆师范大学学报（自然科学版）》2016年第6期69-71,共3页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11271301;No.11471226)

摘　　要：一个群G被称为核(m)-群当且仅当对G的任意子群H,︱H∶H_G︱至多可以表示成m个素数的乘积。证明了如果有限群G是核(m)-群,那么G是可解群,且G的Fitting子群在G中的指数至多是5个素数的乘积。进一步证明了如果有限超可解群G是有限核(2)-群,且群G存在极小正规子群N是阶为p3的初等交换子群,那么则存在素数p,q,使得G有交换正规子群A满足︱G∶A︱|2pq,并且G至多只有4个互不同构的西洛子群不正规。A group Gis called a core（m）-group if and only if│H ∶HG │is a product of at most m prime numbers for each subgroup H ≤G.In this paper,it is proved that the index of the Fitting subgroup in anite core（2）-group Gisa product of at most5 prime numbers.Furthermore,it is also proved that if a supersoluble group Gis a finite core（2）-group which has a minimal normal subgroup N of order p^3,then there exist prime numbers p,q such that│G∶A││2pq for a normal abelian subgroup Aof Gand G has at most four non-isomorphic Slyow subgroups which are not normal.

关 键 词：核(m)-群 可解群 FITTING子群 

分 类 号：O152.1[理学—数学]