Group Homomorphisms: Kernels, Images, and Normal Subgroups

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Explores group homomorphisms, constructing isomorphisms between groups using generators and relations.

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

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

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

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

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

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

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

Explores group morphisms, kernels, and injectivity in group theory.

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