Direct Sums: Abelian Groups

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Group Cohomology

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Abelian Groups: Free Abelian Groups

Explores free abelian groups, homomorphisms, and exact sequences in group theory.

Group Theory: Verification

Covers the verification of constructions in the context of abelian groups and Sylow subgroups.

Direct Sums Arithmetic

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

Algebra: Group Actions and Direct Products

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

Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Direct Products in Group Theory

Explores direct products in group theory, including semi-direct products and group properties.

Direct Sums of Abelian Groups

Covers direct sums of abelian groups, group actions, and vector spaces, including coproducts and homomorphisms.

Finite Cas X and Notations

Introduces Lemma 1.14 for finite sets in Ab and discusses notations and properties of direct sums.

Endomorphisms and automorphisms of totally disconnected locally compact groups V

Explores endomorphisms and automorphisms of totally disconnected locally compact groups, emphasizing surjective homomorphisms and free abelian groups.