Some Polynomials over Q(t) and Their Galois Groups

Examples of polynomials with Galois group over Q(t) corresponding to every transitive group through degree eight are calculated, constructively demonstrating the existence of an infinity of extensions with each Galois group over Q through degree eight. The methods used, which for the most part have...

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Veröffentlicht in:	Mathematics of computation 2000-04, Vol.69 (230), p.775-796
1. Verfasser:	Smith, Gene Ward
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Degrees of polynomials Discriminants Exact sciences and technology Field theory and polynomials Infinity Integers Mathematical functions Mathematical tables Mathematics Polynomials Rational functions Sciences and techniques of general use
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Zusammenfassung:	Examples of polynomials with Galois group over Q(t) corresponding to every transitive group through degree eight are calculated, constructively demonstrating the existence of an infinity of extensions with each Galois group over Q through degree eight. The methods used, which for the most part have not appeared in print, are briefly discussed.
ISSN:	0025-5718 1088-6842
DOI:	10.1090/s0025-5718-99-01160-6