有限群的换位子群的分解  

Decomposition of Commutator Subgroup of Finite Group

作　　者：晋珺 Jin Jun(Department of mathematics Jinzhong University,Yuci Shanxi 030619)

机构地区：[1]晋中学院数学系,山西晋中030619

出　　处：《长治学院学报》2022年第2期13-15,共3页Journal of Changzhi University

摘　　要：设G为有限群,A和B为G的子群,在G=AB且[A,B]=1条件下,利用换位子群的相关性质证明了G的换位子群G′=A′B,进一步,如果有A∩B=1,则G′∩A=A,G′∩B=B,,并利用矩阵构造群进行了结论的验证。Let G be a fnite group,and A,B be its subgroups.It is proved that the commutator subgroup of G satisfies G'=A'B'under the condition ofG=A B and[A,B]=1.Furthermore,if A∩B=1,it is concluded thatG′=A′B,G′∩B=B′At last,the conclusion is validated through a group composed of two matrices.

关 键 词：有限群 换位子群 分解 矩阵 

分 类 号：O152.1[理学—数学]