The structure of a group of permutation polynomials

Gary Lee Mullen; Harald Niederreiter

doi:10.1017/S1446788700023016

The structure of a group of permutation polynomials

Gary Lee Mullen, Harald Niederreiter

Mathematics

Research output: Contribution to journal › Article

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 - Jan 1 1985

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1017/S1446788700023016

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Mullen, G. L., & Niederreiter, H. (1985). The structure of a group of permutation polynomials. Journal of the Australian Mathematical Society, 38(2), 164-170. https://doi.org/10.1017/S1446788700023016

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