2S 4 * Q 8-extensions

Teresa Crespo

A chapter in Algebra, Arithmetic and Geometry with Applications, 2004, pp 263-272 from Springer

Abstract: Abstract Let 2S 4 * Q 8 be the central product of a double cover 2S 4 of the symmetric group S 4 and the quaternion group Q 8. We consider the Galois embedding problem given by 2S 4 * Q 8 as a double cover of the direct product S 4 × V 4 of the symmetric group S 4 and the Klein group V 4 over a field K of characteristic different from 2. If 2 or −2 is a square in K, we give a general formula for the solutions to this embedding problem, whenever it is solvable, in terms of quadratic forms. This result answers a question raised by Abhyankar.

Keywords: Quadratic Form; Symmetric Group; Galois Group; Double Cover; Galois Extension (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18487-1_15

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DOI: 10.1007/978-3-642-18487-1_15

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