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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

The construction of solvable polynomials


Author: Harold M. Edwards
Journal: Bull. Amer. Math. Soc. 46 (2009), 397-411
MSC (2000): Primary 11R32, 11R37, 11R18
Published electronically: March 26, 2009
Erratum: Bull. Amer. Math. Soc. 46 (2009), 703-704.
MathSciNet review: 2507276
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Abstract: Although Leopold Kronecker's 1853 paper ``On equations that are algebraically solvable'' is famous for containing his enunciation of the Kronecker-Weber theorem, its main theorem is an altogether different one, a theorem that reduces the problem of constructing solvable polynomials of prime degree $ \mu$ to the problem of constructing cyclic polynomials of degree $ \mu-1$. Kronecker's statement of the theorem is sketchy, and he gives no proof at all. There seem to have been very few later treatments of the theorem, none of them very clear and none more recent than 1924. A corrected version and a full proof of the theorem are given. The main technique is a constructive version of Galois theory close to Galois's own.


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Additional Information

Harold M. Edwards
Affiliation: Department of Mathematics, New York University, 251 Mercer St., New York, New York 10012

DOI: http://dx.doi.org/10.1090/S0273-0979-09-01253-1
PII: S 0273-0979(09)01253-1
Keywords: Galois theory, solvable polynomials, Kronecker-Weber
Received by editor(s): November 21, 2008
Received by editor(s) in revised form: January 13, 2009
Published electronically: March 26, 2009
Article copyright: © Copyright 2009 American Mathematical Society