Lagrange Galois SolvablePermutationGroups Évariste Galois and Solvable Permutation Groups David A.Cox DepartmentofMathematics AmherstCollege [email protected] Bilbao May2012 Lagrange Galois SolvablePermutationGroups Prologue MostmathematiciansknowaboutGalois: Heintroducedthe conceptof group. Hecreated Galoistheory. Hedefinedfinitefields. ThisTalk We will learnsome oftheamazingotherthingsGaloisdid, especially hiswork onsolvablepermutationgroups. Lagrange Galois SolvablePermutationGroups Prologue MostmathematiciansknowaboutGalois: Heintroducedthe conceptof group. Hecreated Galoistheory. Hedefinedfinitefields. ThisTalk We will learnsome oftheamazingotherthingsGaloisdid, especially hiswork onsolvablepermutationgroups. Lagrange Galois SolvablePermutationGroups Prologue MostmathematiciansknowaboutGalois: Heintroducedthe conceptof group. Hecreated Galoistheory. Hedefinedfinitefields. ThisTalk We will learnsome oftheamazingotherthingsGaloisdid, especially hiswork onsolvablepermutationgroups. Lagrange Galois SolvablePermutationGroups Prologue MostmathematiciansknowaboutGalois: Heintroducedthe conceptof group. Hecreated Galoistheory. Hedefinedfinitefields. ThisTalk We will learnsome oftheamazingotherthingsGaloisdid, especially hiswork onsolvablepermutationgroups. Lagrange Galois SolvablePermutationGroups Outline 1 Lagrange ThreeSnapshots 2 Galois FourSnapshots 3 SolvablePermutationGroups Primitive Equations TheAffine LinearGroup FiniteFields TheMainTheorem Lagrange Galois SolvablePermutationGroups Outline 1 Lagrange ThreeSnapshots 2 Galois FourSnapshots 3 SolvablePermutationGroups Primitive Equations TheAffine LinearGroup FiniteFields TheMainTheorem Lagrange Galois SolvablePermutationGroups Outline 1 Lagrange ThreeSnapshots 2 Galois FourSnapshots 3 SolvablePermutationGroups Primitive Equations TheAffine LinearGroup FiniteFields TheMainTheorem Lagrange Galois SolvablePermutationGroups Three Snapshots from Lagrange In 1770,Lagrangewrotethe wonderfulpaper: Réflexionssurla résolutiondeséquations which introducedmanyofthekey playersofgrouptheoryand Galoistheory. We will givethree excerpts from thispaperto showhow Lagrangelaidthe foundationfor whatGaloisdid. Lagrange Galois SolvablePermutationGroups Three Snapshots from Lagrange In 1770,Lagrangewrotethe wonderfulpaper: Réflexionssurla résolutiondeséquations which introducedmanyofthekey playersofgrouptheoryand Galoistheory. We will givethree excerpts from thispaperto showhow Lagrangelaidthe foundationfor whatGaloisdid.