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Automorphisms of congruence function fields

1991; Mathematical Sciences Publishers; Volume: 150; Issue: 1 Linguagem: Inglês

10.2140/pjm.1991.150.167

1945-5844

Martha Rzedowski–Calderón, Gabriel Villa–Salvador,

Analytic Number Theory Research

Let k be a finite field.For a function field K over k and m > 3, it is proven that there are infinitely many non-isomorphic function fields L such that L/K is a separable extension of degree m and Aut£ L -{Id}.It is also shown that for a finite group G, there are infinitely many non-isomorphic function fields L/k such that Aut* L = G.Finally, given any finite nilpotent group G such that |G| > 1 and (|<7|, \k\ -1) = 1 and any function field K over k 9 there are infinitely many non-isomorphic function fields L over k with Gal(L/K) = Aut* L £* G.