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The structure of a group of permutation polynomials. (English) Zbl 0563.20007

The group of all permutations of the finite field of odd order q of the form \(x\mapsto ax^{n+1}+bx\), where \(n=(q-1)/2\), is shown to be isomorphic to the regular wreath product \({\mathbb{Z}}_ n\wr {\mathbb{Z}}_ 2\) of order \(2n^ 2\).
Reviewer: A.M.Cohen

MSC:

20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
11T06 Polynomials over finite fields
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