Lectures related to Groupes résolubles: Quotients and Subgroups

Solvable Groups: Part 1

Covers the concept of solvable groups and their decomposition into abelian pieces, exploring various properties and examples.

Subgroups and Cosets: Lagrange's Theorem

Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.

Automorphism Groups: Trees and Graphs III

Explores automorphism groups of trees and graphs, including actions on trees and group homomorphisms.

Subsets and subgroups associated with an action

Explores subsets and subgroups related to group actions on sets.

Second Isomorphism Theorem

Delves into the second isomorphism theorem in group theory, emphasizing subgroup relationships and quotient groups.

Group Theory: Quotients of Group

Covers normal subgroups, quotient groups, homomorphisms, and the categorical viewpoint in group theory.

Group Presentation of S3

Covers the group presentation of S3, normal subgroups, generators, relations, quotient groups, and injective homomorphisms.

Subsets and subgroups associated with an action

Explores subsets, subgroups, actions, fixed points, stabilizers, orbits, and bijections in group theory.

Normal Subgroups and Quotients

Introduces normal subgroups, group quotients, and their applications in group theory.

Applications of Lagrange's Theorem

Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.

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Dihedral Group: Symmetries and Cosets

Explores the symmetries of a regular n-gon, normal subgroups, cosets, and Lagrange's theorem.

Categorical Perspective: Group Quotients

Explores the categorical sense of constructing a group quotient by a normal subgroup, showing it as a specific example of a more general construction.

Isomorphism Theorems: Quotients of Group

Explores the isomorphism theorems for quotient groups and the concept of surjective homomorphisms.

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Group Presentations

Covers the concept of group presentations using generators and relations to define groups.

Group Homomorphisms: Kernels, Images, and Normal Subgroups

Explores group homomorphisms, kernels, images, and normal subgroups, using the dihedral group D_n as an example.

Combinatorial Group Theory

Introduces combinatorial group theory, emphasizing group presentations, normal subgroups, and group quotients.

Symmetric Group: Cycle Notation

Explores the symmetric group, emphasizing cycle notation and group properties.

Lagrange's Theorem: Applications and Homomorphisms

Covers Lagrange's theorem, group homomorphisms, congruence classes, and normal subgroups.