How often can a finite group be realized as a Galois group over a field?

DOI10.1007/S002290050171zbMath0976.12004OpenAlexW2043147908MaRDI QIDQ1301743

Alexander Prestel, Christian U. Jensen

Publication date: 13 January 2002

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002290050171

zbMATH Keywords

Galois groupabelian groupnon-abelian groupsrealization multiplicityabelian \(p\)-groupabsolute realization multiplicity

Mathematics Subject Classification ID

Galois theory (11R32) Separable extensions, Galois theory (12F10)

Related Items (5)

A recursive description of pro-\(p\) Galois groups ⋮ On the indecomposability of a remarkable new family of modules appearing in Galois theory ⋮ Parameterizing solutions to any Galois embedding problem over \(\mathbb{Z}/p^n\mathbb{Z}\) with elementary \(p\)-abelian kernel ⋮ $p$-groups have unbounded realization multiplicity ⋮ Arithmetic properties encoded in the Galois module structure of \(K^\times / K^{\times p^m}\)

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