How often can a finite group be realized as a Galois group over a field?
- Cite this article as:
- Jensen, C. & Prestel, A. manuscripta math. (1999) 99: 223. doi:10.1007/s002290050171
Let G be any finite group and \(\) any class of fields. By \(\) we denote the minimal number of realizations of G as a Galois group over some field from the class \(\). For G abelian and \(\) the class of algebraic extensions of ℚ we give an explicit formula for \(\). Similarly we treat the case of an abelian p-group G and the class \(\) which is conjectured to be the class of all fields of characteristic ≠p for which the Galois group of the maximal p-extension is finitely generated. For non-abelian groups G we offer a variety of sporadic results.
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