Solving solvable quintics
HTML articles powered by AMS MathViewer
- by D. S. Dummit PDF
- Math. Comp. 57 (1991), 387-401 Request permission
Corrigendum: Math. Comp. 59 (1992), 309.
Corrigendum: Math. Comp. 59 (1992), 309.
Abstract:
Let $f(x) = {x^5} + p{x^3} + q{x^2} + rx + s$ be an irreducible polynomial of degree 5 with rational coefficients. An explicit resolvent sextic is constructed which has a rational root if and only if $f(x)$ is solvable by radicals (i.e., when its Galois group is contained in the Frobenius group ${F_{20}}$ of order 20 in the symmetric group ${S_5}$). When $f(x)$ is solvable by radicals, formulas for the roots are given in terms of p, q, r, s which produce the roots in a cyclic order.References
- David S. Dummit and Richard M. Foote, Abstract algebra, Prentice Hall, Inc., Englewood Cliffs, NJ, 1991. MR 1138725
- I. M. Isaacs, Solution of polynomials by real radicals, Amer. Math. Monthly 92 (1985), no. 8, 571–575. MR 812099, DOI 10.2307/2323164
- Emma Lehmer, Connection between Gaussian periods and cyclic units, Math. Comp. 50 (1988), no. 182, 535–541. MR 929551, DOI 10.1090/S0025-5718-1988-0929551-0 H. Weber, Lehrbuch der Algebra. I, Chelsea, New York, 1961.
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Math. Comp. 57 (1991), 387-401
- MSC: Primary 12E12; Secondary 12F10
- DOI: https://doi.org/10.1090/S0025-5718-1991-1079014-X
- MathSciNet review: 1079014