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).
