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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
Abstract
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.
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- Copyright © Canadian Mathematical Society 1991
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