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

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  • Keisuke Hakuta

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.

Suggested Citation

  • Keisuke Hakuta, 2017. "Sign of Permutations Induced by Anick and Nagata-Anick Automorphisms over Finite Fields," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(4), pages 23-29, August.
    • Handle: RePEc:ibn:jmrjnl:v:9:y:2017:i:4:p:23-29
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    More about this item

    Keywords

    Polynomial automorphism; finite field; permutation; Anick automorphism; Nagata-Anick automorphism;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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