Group Theory: Quotients of Group

Related lectures (32)

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Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

Explores the third isomorphism theorem in group theory, focusing on quotient groups and a categorical perspective.

Covers the construction and universal properties of pushouts in group theory.

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

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

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

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

Explores group homomorphisms, emphasizing surjective mappings and their impact on group questions.

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

Covers explicit calculations of push-outs in Ens and the study of induced homomorphisms between quotient groups.