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The Normal Closure of a Quadratic Extension of a Cyclic Quartic Field

Published online by Cambridge University Press:  20 November 2018

Theresa P. Vaughan
Theresa P. Vaughan*
Affiliation:
Department of Mathematics, University of North Carolina at Greensboro, Greensboro, NC 27412, USA
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Abstract

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Pierre Barrucand asks the following question (Unsolved Problems, # ASI 88:04, Banff, May 1988, Richard K. Guy, Ed.; also [2, p. 594]). Let K be a cyclic quartic field, and let ξ be a non-square element of K. Let M be the Galois closure of , and let G be the Galois group Gal(M/Q). Find (1) all possible G, (2) conditions on ξ to have such a G, and (3) a list of all possible subfields of M.

Keywords

12F05quadratic extensioncyclic quartic field
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 5 , 01 October 1991 , pp. 1086 - 1097
Copyright
Copyright © Canadian Mathematical Society 1991

References

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4. Thomas, A.D. and Wood, G.V., Group Tables. Shiva Publishing Ltd., Orpington, Kent, UK, 1980.Google Scholar