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The structure of a group of permutation polynomials

Part of: Structure and classification of infinite or finite groups Metric geometry Permutation groups

Published online by Cambridge University Press:  09 April 2009

Gary L. Mullen  and
Harald Niederreiter
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, 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 dymmetry group of a regular complex polygon.

MSC classification

Secondary: 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures 20E22: Extensions, wreath products, and other compositions 51F15: Reflection groups, reflection geometries
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 2 , April 1985 , pp. 164 - 170
Copyright
Copyright © Australian Mathematical Society 1985

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