A group action on multivariate polynomials over finite fields

作者：Reis Lucas^*

来源：Finite Fields and Their Applications, 2018, 51: 218-237.

DOI：10.1016/j.ffa.2018.01.011

• Finite fields
• Invariant theory
• Group action
• Multivariate polynomials

Let F-q be the finite field with q elements, where q is a power of a prime p. Recently, a particular action of the group GL(2)(F-q) on irreducible polynomials in F-q [x] has been introduced and many questions concerning the invariant polynomials have been discussed. In this paper, we give a natural extension of this action on the polynomial ring F-q [x(1), . . . ,x(n)] and study the algebraic properties of the invariant elements.

• 出版日期2018-5