The structure of a group of permutation polynomials

Gary L. Mullen; Harald Niederreiter

doi:10.1017/S1446788700023016

The structure of a group of permutation polynomials

Gary L. Mullen, Harald Niederreiter

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

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

Original language	English (US)
Pages (from-to)	164-170
Number of pages	7
Journal	Journal of the Australian Mathematical Society
Volume	38
Issue number	2
DOIs	https://doi.org/10.1017/S1446788700023016
State	Published - Mar 1985

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1017/S1446788700023016

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AB - 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, b ∊ Fq. 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 symmetry group of a regular complex polygon.

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The structure of a group of permutation polynomials

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