Quotient Groups: Homomorphisms and Isomorphisms

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Group Homomorphisms

Explores group homomorphisms, isomorphisms, and generators in abstract algebra.

Groups and Homomorphisms

Covers Euler's totient function, group theory, homomorphisms, and group isomorphisms.

Group Direct Sums in Group Theory

Explores direct sums in group theory, focusing on abelian groups and their implications.

Quotient Groups and Homomorphisms

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

Group Theory: Quotients of Group

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

Two Definitions of Group Action

Explores two definitions of group action on a set, focusing on properties and applications.

Group Actions: Theory and Examples

Explores concrete examples of group actions on sets, focusing on actions that do not change the set.

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.

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.

Classification of Extensions

Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.