Group Quotients: Push-out Uniqueness

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Explores small order groups, group morphisms, and the second isomorphism theorem.

Explores abelian groups from a categorical perspective, discussing the coproduct construction.

Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.

Explores Coxeter groups, emphasizing generators, relations, and unique presentations in group theory.

Demonstrates the existence of direct sums of abelian groups and covers propositions and proofs related to their uniqueness.

Covers group actions, conjugacy classes, centralizers, direct products, and finite abelian groups.

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

Covers group theory concepts like isomorphism and semi-direct product through examples and proofs.

Explores the arithmetic of direct sums in group theory, discussing conditions for equality.

Explores the concept of direct sums in abelian groups, emphasizing the universal property and homomorphisms.