次正规嵌入子群与有限群的可解性(Ⅰ)  

Subnormally Embedded Subgroups and Solvability of Finite Groups

作　　者：杨立英[1] 韦华全[1] 黄琼[1] 钟国[1] 马儇龙[1] 

机构地区：[1]广西师范学院数学科学学院,广西南宁530023

出　　处：《广西师范学院学报（自然科学版）》2013年第4期18-21,共4页Journal of Guangxi Teachers Education University(Natural Science Edition)

基　　金：国家自然科学基金(10961007;11161006);广西自然科学基金(0991102;0991101);广西教育厅科研基金

摘　　要：证明了,设P是群G的Sylow 2-子群,若P的极大子群都在G中次正规嵌入,则G可解;若群G的Sylow 2-子群的循环子群均在G中次正规嵌入,则G可解;设M为群G的幂零极大子群或M为群G的内2-幂零极大子群,若M的Sylow 2-子群的极大子群都在G中次正规嵌入,则G可解.Let P be a Sylow 2-subgroup of a group G I.f the maximal subgroup of P is subnormal-ly embedded in G ,then G is solvable I.f a cyclic subgroup of Sylow 2-subgroup of a group G is subnor-mally embedded in G .then G is solvable .Let M be a nilpotnent maximal subgroup of a group G or M be an inner 2-nilpotent maximal subgroup of a group G ,if the maximal subgroup of Sylow 2-subgroup of M is subnormally embedded in G ,then G is solvable .

关 键 词：可解群 次正规嵌入子群 SYLOW 2-子群 极大子群 循环子群 

分 类 号：O152.1[理学—数学]