Abel–Ruffini theorem

The set of Abel - Ruffini says that a general polynomial equation of fifth degree or higher not by radicals, ie root expressions, is resolvable.

History

The first proof of this theorem was published by Paolo Ruffini in 1799. However, this evidence was incomplete and was also largely ignored. A complete proof was in 1824 Niels Henrik Abel.

Deeper insight into the problem a little later granted the Galois Galois theory developed by Évariste. Using the general results of Galois theory must be shown to prove the theorem of Abel- Ruffini only two points:

• The general equation of the fifth degree (ie the equation with variables as coefficients ) than Galois group the symmetric group S5
• The symmetric group S5 is not solvable, because it contains as the only real normal subgroup of the alternating group A5 of order 60, and this is easy.