Automorphisms of Finite Fields
نویسنده
چکیده
Let F be a finite field, and 4: F* + E a surjective group homomorphism from the multiplicative group F* of F to a non-trivial abelian group E. A theorem of McConnel (Acta Arith. 8 (1963) 127-151) describes the permutations e of F with the property that d(ux uy) = d(x y) for all X, j’ E F, .Y #J. We give a short proof of this theorem, based on an argument of Bruen and Levinger (Canad. J. Math. 25 (1973), 1060-1065). In addition, we describe the permutations c of F for which there exists a permutation K of E with the property that &U-X q) = K&X 4’) for all X, ~2 E F, x # y. Finally, we prove a result about automorphisms of the norm form of an arbitrary finite extension of fields. ,(’ 1990 Academic PI~SS, IW
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تاریخ انتشار 2003