Galois realizability of non-split group extensions of \(C_{2}\) by (\(C_{2})^{r}\times (C_{4})^{s}\times (D_{4})^{t}\).
type: Item
instance of: scholarly article
title: Galois realizability of non-split group extensions of \(C_{2}\) by (\(C_{2})^{r}\times (C_{4})^{s}\times (D_{4})^{t}\).
zbMATH Open document ID: 1043.12004
author: H. G. Grundman
author: Grisha L. Stewart
published in: Journal of Algebra
publication date: 2004-03-14T00:00:00Z
review text: The paper under review considers embedding problems of field extensions given by an exact sequence \(1\rightarrow C_2\rightarrow G\rightarrow (C_2)^r\times (C_4)^s\times (D_4)^t\rightarrow 1\), where \(C_2,C_4\) are cyclic groups of order 2, resp.~4 and \(D_4\) denotes the dihedral group of order 8. Theorem 1 gives the obstruction to this embedding problem in terms of tensor products of quaternion algebras defined by certain subfields. As an application we get obstructions to the realizability of 13 groups of order 32 which were not previously known.
reviewed by: Martin Epkenhans
Mathematics Subject Classification ID: 12F12
zbMATH DE Number: 2055637
zbMATH Keywords: realizability
zbMATH Keywords: embedding problems
zbMATH Keywords: Galois extension
describes a project that uses: GAP
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2003.09.017
OpenAlex ID: W1995312398
cites work: Orthogonal representations of Galois groups, Stiefel-Whitney classes and Hasse-Witt invariants.
cites work: Q4440900
cites work: Groups of order 16 as Galois groups
cites work: Q5586486
cites work: Explicit Classifications of Some 2-Extensions of a Field of Characteristic Different from 2
cites work: On 2-Groups as Galois Groups
cites work: Extra-Special Groups of Order 32 as Galois Groups
cites work: QUADRATIC CORESTRICTION, -EMBEDDING PROBLEMS, AND EXPLICIT CONSTRUCTION
cites work: Q3882616
DOI: 10.1016/J.JALGEBRA.2003.09.017
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description: scientific article; zbMATH DE number 2055637