Groups of Polynomial Permutations over Finite Commutative Rings
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O156.2

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    Abstract:

    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.

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Cite this article as: PAN Jia-Kun, ZHANG Qi-Fan. Groups of Polynomial Permutations over Finite Commutative Rings [J]. J Sichuan Univ: Nat Sci Ed, 2016, 53: 275.

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History
  • Received:April 24,2015
  • Revised:May 19,2015
  • Adopted:May 25,2015
  • Online: December 02,2016
  • Published: