Groups of order 16 as Galois groups

zbMath0838.12004MaRDI QIDQ1906659

John R. Swallow, Helen G. Grundman, Tara L. Smith

Publication date: 25 February 1996

Published in: Expositiones Mathematicae (Search for Journal in Brave)

zbMATH Keywords

inverse Galois theoryGalois 2-groupsrealizability of small 2-groups

Mathematics Subject Classification ID

Inverse Galois theory (12F12)

Related Items (18)

On Steinitz classes, realizable Galois module classes and embedding problems for non-abelian extensions of degree a power of 2 ⋮ On the computation of the trace form of some Galois extensions ⋮ Galois realizability of a central \(C_4\)-extension of \(D_8\) ⋮ Unramified quaternion extensions of quadratic number fields ⋮ Parameterizing solutions to any Galois embedding problem over \(\mathbb{Z}/p^n\mathbb{Z}\) with elementary \(p\)-abelian kernel ⋮ Relative Embedding Problems ⋮ Galois realizability of non-split group extensions of \(C_{2}\) by (\(C_{2})^{r}\times (C_{4})^{s}\times (D_{4})^{t}\). ⋮ Relative Galois module structure and Steinitz classes of dihedral extensions of degree 8 ⋮ Embedding obstructions for the generalized quaternion group ⋮ $p$-groups have unbounded realization multiplicity ⋮ Galois realizability of groups of order 64 ⋮ Realizability and automatic realizability of Galois groups of order 32 ⋮ Galois embedding problems with cyclic quotient of order \(p\) ⋮ Embedding obstructions for the dihedral, semidihedral, and quaternion 2-groups ⋮ Note on the rings of integers of certain tame 2-Galois extensions over a number field ⋮ Automatic realization of Galois groups with cyclic quotient of order \(p^n\) ⋮ Automatic realizability of Galois groups of order 16 ⋮ Arithmetic properties encoded in the Galois module structure of \(K^\times / K^{\times p^m}\)

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