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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

1. Hall, M., Jr. and Senior, J.K., The groups of order 2n(n ≥6). Macmillan, 1964.Google Scholar
2. Mollin, R.A., Number Theory and Applications. Kluwer, 1989.Google Scholar
3. van der Waerden, B.L., Modern Algebra. Frederick Ungar Publishing, New York, 1950.Google Scholar
4. Thomas, A.D. and Wood, G.V., Group Tables. Shiva Publishing Ltd., Orpington, Kent, UK, 1980.Google Scholar