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 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 | |
| State | Published - Jan 1 1985 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Mathematics(all)
Cite this
}
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 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 -