(Prior to publication, this paper should be cited as arXiv:1312.2649.)

For any prime power q, let G(q) denote the group of permutations of the finite field F_q which is generated by those permutations that can be written as c → ac^m + bcⁿ  for some 0 < m < n < q  and some nonzero a, b in F_q. 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.

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