Permutations in a Finite Field
نویسنده
چکیده
For q = 5, this was proved to be true by Betti; for q = 7 the corresponding result was verified by Dickson [l, p. 119]. In this note we show very simply that this result holds for all q. Since the totality of permutation polynomials evidently furnishes a representation of the symmetric group on q letters, it will suffice to show that every transposition (Oa) can be generated by means of the special polynomials (1); here a denotes a fixed nonzero number EGF(q). We consider the following polynomial
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تاریخ انتشار 2010