Lectures related to Groupes résolubles: Quotients and Subgroups

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.