Le groupe alterné A5 est un groupe simple : preuve complète

A proof requiring few prerequisites, quite fast, and proving that the alternating group A5 is a simple group. Basically, I adapted to n=5 a proof that An is simple for n greater than 5, which appears in Gardiner, Algebraic Structures. Outline 01:51: Diagram of the proof (H denotes a normal subgroup of A5 not reduced to Id) 04:17: Proof that H=A5 06:28: H contains a 3-cycle 18:25: The 3-cycles generate A5 24:28: The 3-cycles are all conjugate in A5