Concept
Classification of finite simple groups
Related lectures (44)
Monster Group: Representation
Explores the Monster group, a sporadic simple group with a unique representation theory.
Properties of Sylow Subgroups: Group Theory
Explores the beautiful properties of the p-Sylow subgroups of a finite group.
Determinants: Alternate Forms and Symmetrization
Explores alternate forms, symmetric forms, and determinants in linear algebra.
Proper Actions and Quotients
Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.
Algebraic Structures: Small Order Groups
Explores small order groups, group morphisms, and the second isomorphism theorem.
Algebraic Decomposition: Understanding Simple Algebraic Structures
Explores algebraic decomposition, simple structures, irreducibility, and separability in finite degrees.
Existence of Sylow Subgroups: Proof by Recurrence
Demonstrates the existence of p-Sylow subgroups in any finite group using induction and the abelian case.
Abelian p-groups: Groupes abéliens
Focuses on abelian p-groups, demonstrating technical results for classifying finite abelian groups.
Finite Fields and Group Theory
Explores solutions of the 2018 exam, finite fields, group theory, congruences, and polynomial irreducibility in Q[X].
Coxeter Groups: Classification Theorem & Order of F_4
Explores the classification theorem for Coxeter groups and the order of F_4.