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Title: Polynomial Automorphisms Over Finite Fields
Authors: Maubach, Stefan
Keywords: Polynomial Automorphisms
Tame Automorphisms
Affine Spaces Over Finite Fields
Primitive Groups
Issue Date: 2001
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 27, No 4, (2001), 343p-350p
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).
ISSN: 1310-6600
Appears in Collections:Volume 27 Number 4

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