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The structure of a group of permutation polynomials

Published online by Cambridge University Press:  09 April 2009

Gary L. Mullen
Affiliation:
Department of Mathematics The Pennsylvania State UniversityUniversity Park, Pennsylvania 16802, U.S.A.
Harald Niederreiter
Affiliation:
Mathematical InstituteAustrian Academy of Sciences Dr. Ignaz-Seipel-Platz 2 A-1010 Vienna, Austria
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Abstract

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Let Gq be the group of permutations of the finite field Fq of odd order q that can be represented by polynomials of the form ax(q+1)/2 + bx with a, bFq. It is shown that Gq is isomorphic to the regular wreath product of two cyclic groups. The structure of Gq can also be described in terms of cyclic, dicyclic, and dihedral groups. It also turns out that Gq is isomorphic to the dymmetry group of a regular complex polygon.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1985

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