Class Equation and Burnside's Lemma

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Amalgams: Group Pushouts

Covers the concept of amalgams, defining pushouts and quotient groups in group theory.

Group Actions: Examples and Applications

Explores examples of group actions on sets, emphasizing the utility of group actions to understand groups.

Push-out and Quotients

Delves into push-out and quotients in group theory, emphasizing homomorphisms and normal subgroups.

Homomorphism of Groups: Signature

Explores homomorphisms of groups, focusing on the signature sgn and the concept of cycles and transpositions.

Uniqueness of Amalgams

Explores the uniqueness of amalgams in group theory through examples and diagrams.

Hom Functor: Abelian Groups

Explores the Hom functor for abelian groups and its relation to direct sums.

Free Product: Group Theory

Covers the concept of the free product in group theory and how to determine monomorphisms and homomorphisms.

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.

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Quotients de groupe: Un cas particulier

Explores a categorical perspective on group quotients, focusing on a specific case.