### 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 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

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