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

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A subgroup with index 2 is distinguished

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Thomaths 28 : Actions de groupe

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Numerical Representation of data - Arithmetic mean (property 1.2) proof.

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Simple Groups - Abstract Algebra

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Groupe symétrique 3/5 : Ordre

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Le groupe alterné A5 n'admet aucun sous-groupe d'ordre 30

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Langage mathématique - Alain Connes

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Le groupe symétrique. Cours Maths Sup / Maths Spé

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Why you can't solve quintic equations (Galois theory approach) #SoME2

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If Prime Numbers Become Increasingly Rare, Then Why Do They Keep Showing Up In Pairs?

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The Concept So Much of Modern Math is Built On | Compactness

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Abstract Algebra | The Alternating Group

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Groupe symétrique 5/5 : Signature

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The French Do Not Care About Work

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Terry Tao, Ph.D. Small and Large Gaps Between the Primes

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Russell's Paradox - a simple explanation of a profound problem

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Hugo Duminil Copin - Le hasard existe-t-il vraiment?

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Développement d'agrégation : An est simple.

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SOUS-GROUPES DISTINGUÉS

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