Permutation groups generated by binomials

Abstract

Let G(q) be the group of permutations of the finite field F_q which is generated by those permutations that can be written as c-->ac^m+bc^n with 0<m<n<q and a,b in F_q with ab nonzero. We show that there are infinitely many q for which G(q) is the group of all permutations of F_q which fix 0. This resolves a conjecture of Vasilyev and Rybalkin.

13 pages

References in corpus (2)

• Permutation polynomials on F_q induced from bijective Redei functions on subgroups of the multiplicative group of F_q
• Permutation polynomials induced from permutations of subfields, and some complete sets of mutually orthogonal latin squares