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Gábor Korchmáros Maria Montanucci Pietro Speziali 《Journal of Pure and Applied Algebra》2018,222(7):1810-1826
Let be the algebraic closure of a finite field of odd characteristic p. For a positive integer m prime to p, let be the transcendence degree 1 function field defined by . Let and . The extension is a non-Galois extension. Let K be the Galois closure of F with respect to H. By Stichtenoth [20], K has genus , p-rank (Hasse–Witt invariant) and a -automorphism group of order at least . In this paper we prove that this subgroup is the full -automorphism group of K; more precisely where Δ is an elementary abelian p-group of order and D has an index 2 cyclic subgroup of order . In particular, , and if K is ordinary (i.e. ) then . On the other hand, if G is a solvable subgroup of the -automorphism group of an ordinary, transcendence degree 1 function field L of genus defined over , then ; see [15]. This shows that K hits this bound up to the constant .Since has several subgroups, the fixed subfield of such a subgroup N may happen to have many automorphisms provided that the normalizer of N in is large enough. This possibility is worked out for subgroups of Δ. 相似文献
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