A result of Hermite and equations of degree 5 and 6
JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)
ID 524265
Author(s) Kraft, Hanspeter
Author(s) at UniBasel Kraft, Hanspeter
Year 2006
Title A result of Hermite and equations of degree 5 and 6
Journal Journal of Algebra
Volume 297
Number 1
Pages / Article-Number 234-253
Abstract 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.
Publisher Elsevier
ISSN/ISBN 0021-8693
edoc-URL http://edoc.unibas.ch/dok/A5842773
Full Text on edoc Restricted
Digital Object Identifier DOI 10.1016/j.jalgebra.2005.04.015
ISI-Number WOS:000236078300012
Document type (ISI) Article

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