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Solving Polynomials by Radicals with Roots of Unity in Minimum Depth

Gwoboa Horng and Ming-Deh Huang
Mathematics of Computation
Vol. 68, No. 226 (Apr., 1999), pp. 881-885
Stable URL: http://www.jstor.org/stable/2585063
Page Count: 5
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Solving Polynomials by Radicals with Roots of Unity in Minimum Depth
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Abstract

Let k be an algebraic number field. Let α be a root of a polynomial f ∈ k[x] which is solvable by radicals. Let L be the splitting field of α over k. Let n be a natural number divisible by the discriminant of the maximal abelian subextension of L, as well as the exponent of G(L/k), the Galois group of L over k. We show that an optimal nested radical with roots of unity for α can be effectively constructed from the derived series of the solvable Galois group of L(ζn) over k(ζn).

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