Sign of Permutations Induced by Anick and Nagata-Anick Automorphisms over Finite Fields

Abstract

In this paper, we investigate the sign of permutations induced by the Anick automorphism and the Nagata-Anick automorphism over finite fields. We shall prove that if the Anick automorphism and the Nagata-Anick automorphism are defined over a prime field of characteristic two, they induce odd permutations, and otherwise, they induce even permutations.