On permutations induced by tame automorphisms over finite fields
Abstract
The present paper deals with permutations induced by tame automorphisms over finite fields. The first main result is a formula for determining the sign of the permutation induced by a given elementary automorphism over a finite field. The second main result is a formula for determining the sign of the permutation induced by a given affine automorphism over a finite field. We also give a combining method of the above two formulae to determine the sign of the permutation induced by a given triangular automorphism over a finite field. As a result, for a given tame automorphism over a finite field, if we know a decomposition of the tame automorphism into a finite number of affine automorphisms and elementary automorphisms, then one can easily determine the sign of the permutation induced by the tame automorphism.
Keywords
Cite
@article{arxiv.1705.01838,
title = {On permutations induced by tame automorphisms over finite fields},
author = {Keisuke Hakuta},
journal= {arXiv preprint arXiv:1705.01838},
year = {2017}
}
Comments
15 pages, accepted for publication in Acta Mathematica Vietnamica