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