A Note on the Quaternion Group as Galois Group

DOI10.2307/2047779zbMath0697.10020OpenAlexW4239738148MaRDI QIDQ3474712

Roger Ware

Publication date: 1990

Full work available at URL: https://doi.org/10.2307/2047779

zbMATH Keywords

Witt ringquadratic formsGalois extensionpro-2-Galois groupsquaternionic Galois extensionstotally positive extension

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) General binary quadratic forms (11E16)

Related Items (3)

Constructing quaternionic fields ⋮ Embedding obstructions for the generalized quaternion group ⋮ Automatic realizability of Galois groups of order 16

Cites Work

• Unnamed Item
• Quadratic forms and pro 2-groups. II: The Galois group of the Pythagorean closure of a formally real field
• The Witt invariant of the form \(\text{Tr}(x^ 2)\)
• Rigid elements, valuations, and realization of Witt rings
• A recursive description of the maximal pro-2 Galois group via Witt rings
• Quaternion fields inside Pythagorean closure
• When are Witt rings group rings? II
• Orthogonal representations of Galois groups, Stiefel-Whitney classes and Hasse-Witt invariants.
• Konstruktion von galoisschen Körpern der Charakteristik p zu vorgegebener Gruppe der Ordnung pf.

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