A result of Hermite and equations of degree 5 and 6

Kraft, Hanspeter. (2006) A result of Hermite and equations of degree 5 and 6. Journal of Algebra, 297 (1). pp. 234-253.

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A classical result from 1861 due to Hermite says that every separable equation of degree 5 can be transformed into an equation of the form x^5 + b x^3 + c x + d = 0. Later this was generalized to equations of degree 6 by Joubert. We show that both results can be understood as an explicit analysis of certain covariants of the symmetric groups S_5 and S_6. In case of degree 5, the classical invariant theory of binary forms of degree 5 come into play whereas in degree 6 the existence of an outer automorphism of S_6 plays an essential role.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Algebra (Kraft)
UniBasel Contributors:Kraft, Hanspeter
Item Type:Article, refereed
Article Subtype:Research Article
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:28 Sep 2017 05:58
Deposited On:08 Jun 2012 06:47

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