A result of Hermite and equations of degree 5 and 6
| dc.creator | Kraft, Hanspeter | |
| dc.date | 2004-03-19 | |
| dc.date | 2006-09-09 | |
| dc.date.accessioned | 2026-07-07T06:36:02Z | |
| dc.date.available | 2026-07-07T06:36:02Z | |
| dc.description | 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 comes into play whereas in degree 6 the existence of an outer automorphism of S_6 plays an essential role. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0403323 | |
| dc.identifier | http://arxiv.org/abs/math/0403323 | |
| dc.identifier | J. Algebra 297 (2006), 234-253 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99967 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Representation Theory | |
| dc.subject | 13A50; 14R20; 20C30; 20B30; 12F05 | |
| dc.title | A result of Hermite and equations of degree 5 and 6 | |
| dc.type | text |