The structure of a group of permutation polynomials

Gary Lee Mullen, Harald Niederreiter

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)164-170
Number of pages7
JournalJournal of the Australian Mathematical Society
Volume38
Issue number2
DOIs
StatePublished - Jan 1 1985

Fingerprint

Permutation Polynomial
Cyclic group
Isomorphic
Dihedral group
Wreath Product
Symmetry Group
Polygon
Galois field
Permutation
Odd
Polynomial
Form

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

@article{ab182591f8d047b5ac311beba73c4949,
title = "The structure of a group of permutation polynomials",
abstract = "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.",
author = "Mullen, {Gary Lee} and Harald Niederreiter",
year = "1985",
month = "1",
day = "1",
doi = "10.1017/S1446788700023016",
language = "English (US)",
volume = "38",
pages = "164--170",
journal = "Journal of the Australian Mathematical Society",
issn = "1446-7887",
publisher = "Cambridge University Press",
number = "2",

}

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

In: Journal of the Australian Mathematical Society, Vol. 38, No. 2, 01.01.1985, p. 164-170.

Research output: Contribution to journalArticle

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 -