Group Homomorphisms: Kernels, Images, and Normal Subgroups

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (32)

Page 2 of 4

Groups: Definitions, Properties, and Homomorphisms

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.

Group Theory: Quotients of Group

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

Applications of Lagrange's Theorem

Explores Lagrange's theorem applications in group theory and arithmetic, focusing on subgroups, cosets, quotient groups, and homomorphisms.

Symmetries in Regular Polygons

Delves into the symmetries of regular polygons, including the dihedral group and left cosets in a finite group.

Quotient Groups and Homomorphisms

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

Permutations and Adjacency

Explores permutations preserving adjacency, linear transformations, groups, and sub-groups.

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.

Push-out and Quotients

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

Group Presentation of S3

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

Pushouts in Group Theory: Universal Properties Explained

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