Polynomial Automorphisms Over Finite Fields

Maubach, Stefan. "Polynomial Automorphisms Over Finite Fields." Serdica Mathematical Journal 27.4 (2001): 343-350. <http://eudml.org/doc/11544>.

@article{Maubach2001,
abstract = {It is shown that the invertible polynomial maps over a finite field Fq , if looked at as bijections Fn,q −→ Fn,q , give all possible bijections in the case q = 2, or q = p^r where p > 2. In the case q = 2^r where r > 1 it is shown that the tame subgroup of the invertible polynomial maps gives only the even bijections, i.e. only half the bijections. As a consequence it is shown that a set S ⊂ Fn,q can be a zero set of a coordinate if and only if #S = q^(n−1).},
author = {Maubach, Stefan},
journal = {Serdica Mathematical Journal},
keywords = {Polynomial Automorphisms; Tame Automorphisms; Affine Spaces Over Finite Fields; Primitive Groups; polynomial automorphisms; tame automorphisms; affine spaces over finite fields; automorphism group; bijections; set of zeros; primitive subgroup of the symmetric group},
language = {eng},
number = {4},
pages = {343-350},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Polynomial Automorphisms Over Finite Fields},
url = {http://eudml.org/doc/11544},
volume = {27},
year = {2001},
}

TY - JOUR
AU - Maubach, Stefan
TI - Polynomial Automorphisms Over Finite Fields
JO - Serdica Mathematical Journal
PY - 2001
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 27
IS - 4
SP - 343
EP - 350
AB - It is shown that the invertible polynomial maps over a finite field Fq , if looked at as bijections Fn,q −→ Fn,q , give all possible bijections in the case q = 2, or q = p^r where p > 2. In the case q = 2^r where r > 1 it is shown that the tame subgroup of the invertible polynomial maps gives only the even bijections, i.e. only half the bijections. As a consequence it is shown that a set S ⊂ Fn,q can be a zero set of a coordinate if and only if #S = q^(n−1).
LA - eng
KW - Polynomial Automorphisms; Tame Automorphisms; Affine Spaces Over Finite Fields; Primitive Groups; polynomial automorphisms; tame automorphisms; affine spaces over finite fields; automorphism group; bijections; set of zeros; primitive subgroup of the symmetric group
UR - http://eudml.org/doc/11544
ER -