Solving solvable quintics

Author:
D. S. Dummit

Journal:
Math. Comp. **57** (1991), 387-401

MSC:
Primary 12E12; Secondary 12F10

Corrigendum:
Math. Comp. **59** (1992), 309.

Corrigendum:
Math. Comp. **59** (1992), 309.

MathSciNet review:
1079014

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Abstract: Let 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 is solvable by radicals (i.e., when its Galois group is contained in the Frobenius group of order 20 in the symmetric group ). When 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.

**[1]**David S. Dummit and Richard M. Foote,*Abstract algebra*, Prentice Hall, Inc., Englewood Cliffs, NJ, 1991. MR**1138725****[2]**I. M. Isaacs,*Solution of polynomials by real radicals*, Amer. Math. Monthly**92**(1985), no. 8, 571–575. MR**812099**, 10.2307/2323164**[3]**René Schoof and Lawrence C. Washington,*Quintic polynomials and real cyclotomic fields with large class numbers*, Math. Comp.**50**(1988), no. 182, 543–556. MR**929552**, 10.1090/S0025-5718-1988-0929552-2**[4]**H. Weber,*Lehrbuch der Algebra*. I, Chelsea, New York, 1961.

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DOI:
https://doi.org/10.1090/S0025-5718-1991-1079014-X

Article copyright:
© Copyright 1991
American Mathematical Society