摘要
发现任意集合A上一个由非一一变换关于变换乘法构成的群与A的某个子集上一个变换群的同构 ;证明A上一个非一一变换f能出现在一个由A上变换构成的乘法群中当且仅当f(A)上的限制ResAf(A) f为f(A)上一一变换 .然后将结论用到矩阵代数中 ,给出数域F上n级矩阵M满足秩M =秩M2 的充要条件 .
We assert here that a group generated by non\|bijective transformations on a set A is isomorphic to a permutation group on a subset of A,and prove that a non bijective transformation f on A occurs in a group consisting of non\|bijective transformations if and only if that the restriction to f(A) of f is bijective.Also with these statements we give the necessary and sufficient conditions for a matrix M on a field F satisfying that the ranks of M and M\+2 are the same.
出处
《首都师范大学学报（自然科学版）》
2003年第2期5-14,共10页
Journal of Capital Normal University：Natural Science Edition
基金
国家自然科学基金项目资助 ( 10 2 710 81)
