### 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) |
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Pages (from-to) | 164-170 |

Number of pages | 7 |

Journal | Journal of the Australian Mathematical Society |

Volume | 38 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1985 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Journal of the Australian Mathematical Society*,

*38*(2), 164-170. https://doi.org/10.1017/S1446788700023016

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*Journal of the Australian Mathematical Society*, vol. 38, no. 2, pp. 164-170. https://doi.org/10.1017/S1446788700023016

**The structure of a group of permutation polynomials.** / Mullen, Gary Lee; Niederreiter, Harald.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The structure of a group of permutation polynomials

AU - Mullen, Gary Lee

AU - Niederreiter, Harald

PY - 1985/1/1

Y1 - 1985/1/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84974220787&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84974220787&partnerID=8YFLogxK

U2 - 10.1017/S1446788700023016

DO - 10.1017/S1446788700023016

M3 - Article

AN - SCOPUS:84974220787

VL - 38

SP - 164

EP - 170

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

SN - 1446-7887

IS - 2

ER -