On a theorem of Carlitz

Details On a theorem of Carlitz On a theorem of Carlitz

2008-10-16

arxiv.org/abs/0810.2834v1

Mathematics

Number Theory

2 pages

Scientific paper

Carlitz proved that, for any prime power q other than 2, the group of all
permutations of the finite field F_q is generated by the permutations induced
by linear polynomials and x^{q-2}. We give a simpler proof and some
consequences. In particular, this result implies that every permutation of F_q
is induced by an exceptional polynomial.

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