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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## 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.

Faculties and Departments: | 05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Algebra (Kraft) |
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UniBasel Contributors: | Kraft, Hanspeter |

Item Type: | Article, refereed |

Article Subtype: | Research Article |

Bibsysno: | Link to catalogue |

Publisher: | Elsevier |

ISSN: | 0021-8693 |

Note: | Publication type according to Uni Basel Research Database: Journal article |

Language: | English |

Identification Number: | |

Last Modified: | 28 Sep 2017 05:58 |

Deposited On: | 08 Jun 2012 06:47 |

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