二元域上一般线性群到任意域上一般线性群的同态  

Homomorphisms from General Linear Groups over the Field of Two Elements to Linear Groups over any Field

作　　者：朱捷[1] 

机构地区：[1]黑龙江科技学院数力系,哈尔滨150027

出　　处：《吉林大学学报（理学版）》2005年第3期268-274,共7页Journal of Jilin University:Science Edition

基　　金：黑龙江省教育厅科学技术项目基金(批准号: 10551283);黑龙江科技学院引进人才科研启动基金(批准号: 04 25)

摘　　要：采用矩阵方法, 描述了二元域F2 上一般线性群GLn(F2 ) (n≥3)到任意域K上一般线性群GLn(K)的同态形式. 当ChK≠2时, 给出了GL3 (F2 )到GL3 (K)的同态形式, 并证明当n≥4时, GLn(F2 )到GLn(K)的同态是平凡的; 当ChK=2且n≥3时, 给出了GLn(F2 )到GLn(K)的同态形式.By using the matrix method, the present paper describes all the homomorphisms from the general linear group GL_n(F_2)(n≥3) over the field F_2 with two elements into the general linear group GL_n(K) over a field K. If Ch K≠2, the characterization of the homomorphisms from GL_3(F_2) into GL_3(K) is given, and it is proved that the homomorphisms from GL_n(F_2) into GL_n(K) are trivial whenever n≥4; if Ch K≠2 and n≥3, homomorphisms from GL_n(F_2) into GL_n(K) are characterized.

关 键 词：域 线性群 对合 同态 

分 类 号：O152.3[理学—数学]