Mullen, Gary L.; Niederreiter, Harald The structure of a group of permutation polynomials. (English) Zbl 0563.20007 J. Aust. Math. Soc., Ser. A 38, 164-170 (1985). 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 Cited in 3 Documents MSC: 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures 11T06 Polynomials over finite fields Keywords:group of permutations of finite field; regular wreath product PDFBibTeX XMLCite \textit{G. L. Mullen} and \textit{H. Niederreiter}, J. Aust. Math. Soc., Ser. A 38, 164--170 (1985; Zbl 0563.20007)