CAJ | 학술논문

设F是一个特征不为2的域,Tn(F)是域F上所有n×n的可逆上三角矩阵组成的群.首先利用矩阵的运算技巧研究了Tn(F)的所有幺幂正规子群的结构,对Tn(F)的任意一个幺幂正规子群给出了一个完全的刻画,即每一个幺幂正规子群都可以由一个元素来生成；然后借助可逆映射在生成元上的作用方式,给出了可逆上三角矩阵群上保幺幂正规子群的双射的具体表达式.
설F시일개특정불위2적역,Tn(F)시역F상소유n×n적가역상삼각구진조성적군.수선이용구진적운산기교연구료Tn(F)적소유요멱정규자군적결구,대Tn(F)적임의일개요멱정규자군급출료일개완전적각화,즉매일개요멱정규자군도가이유일개원소래생성；연후차조가역영사재생성원상적작용방식,급출료가역상삼각구진군상보요멱정규자군적쌍사적구체표체식.
Let F be a field of characteristic not 2,Tn (F) the group consisting of all n × n invertible upper triangular matrices over F.First,the structure of the unipotent normal subgroups of Tn(F) is studied by techniques of matrix calculations.The unipotent normal subgroups of Tn (F) are determined completely,and each unipotent normal subgroup is shown to be generated by one element; Second,using the method of action on the generators by invertible maps,every invertible map on Tn(F) that preserves unipotent normal subgroup is described in an explicit formula.