Solvable Groups: Part 1Covers the concept of solvable groups and their decomposition into abelian pieces, exploring various properties and examples.
Group Presentation of S3Covers the group presentation of S3, normal subgroups, generators, relations, quotient groups, and injective homomorphisms.
Group PresentationsCovers the concept of group presentations using generators and relations to define groups.
Push-out and QuotientsDelves into push-out and quotients in group theory, emphasizing homomorphisms and normal subgroups.
Connected ComponentsCovers the concept of connected components in linear algebraic groups and their relationship to singular groups.
Groupes résolublesExplores solvable groups, group actions, normalizers, and stabilizers in group theory.
Invariant DefinitionsExplores invariant definitions in sets, groups, and automorphisms, including p-divisible groups and free abelian groups.
Finite Abelian GroupsCovers Cauchy's theorem, classification of finite abelian groups, direct product properties, and more.
Sylow Subgroups: Group TheoryExplores the concept of p-subgroups of Sylow in group theory, emphasizing the philosophy of studying mathematical objects 'one prime at a time'.
