%0 Journal Article
%T 有限交换环上的多项式置换群<br>Groups of Polynomial Permutations over Finite Commutative Rings
%A 潘嘉？？
%A 张起帆
%J 四川大学学报 (自然科学版)
%D 2016
%X Sophie Frisch描述了$\mathbb{Z}/p^2\mathbb{Z}$上多项式置换群的结构。 张起帆找到$\mathbb{Z}/p^2\mathbb{Z}$上多项式函数与$\mathbb{Z}/p\mathbb{Z}$上多项式函数的3维向量之间的对应关系。 本文先证明在任意有限交换环$R$上，多项式置换群同构于多项式函数形成的$R$-代数的自同构群。 然后我们用张起帆的对应对Sophie Frisch描述给出一个新的证明。<br>Sophie Frisch characterized the structure of the group of polynomial permutations over $\mathbb{Z}/p^2\mathbb{Z}$. Qifan Zhang found a correspondence between polynomial functions over $\mathbb{Z}/p^2\mathbb{Z}$ and 3-tuples of polynomial functions over $\mathbb{Z}/p\mathbb{Z}$, this paper is giving another proof of [1]. In this paper, we first prove that over any finite commutative ring $R$, the group of polynomial permutations is isomorphic to the automorphism group of the $R$-algebra of the polynomial functions. Then we give an easy proof to the characterization of Sophie Frisch using the correspondence set found by Zhang
%K Witt多项式
%K 置换多项式
%K 半直积
%K 圈积&lt
%K br&gt
%K Witt polynomials
%K permutation polynomials
%K semi-direct product
%K wreath product
%U http://science.ijournals.cn/jsunature_cn/ch/reader/view_abstract.aspx?file_no=Z150205&flag=1