# Polynomial Automorphisms Over Finite Fields

Serdica Mathematical Journal (2001)

- Volume: 27, Issue: 4, page 343-350
- ISSN: 1310-6600

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topMaubach, 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 -

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