Hom Functor: Abelian Groups

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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.

Direct Sums of Abelian Groups

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

Group Theory: Direct Sum of Abelian Groups

Explores the arithmetic of direct sum of abelian groups and the process of turning a monoid into a commutative group.

Finite Cas X and Notations

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

Algebra: Group Actions and Direct Products

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

Direct Products in Group Theory

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

Exact Sequences: Torsion and Divisibility

Explores exact sequences of abelian group homomorphisms and provides examples.

Torsion: Hom Functoriality and Exact Sequences

Explores the concept of torsion in group theory, focusing on its Hom functoriality and its role in exact sequences.

Sylow Subgroups: Structure and Properties

Explores the properties and structure of Sylow subgroups in group theory, emphasizing a theorem-independent approach.

Group Theory - Part 2

Explores Cayley tables, group operations, homomorphisms, Lie groups, and differentiable groups.