Torsion and Divisibility: Abelian Groups

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Demonstrates the existence of p-Sylow subgroups in any finite group using induction and the abelian case.

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

Explores the concept of p-subgroups of Sylow in group theory, emphasizing the philosophy of studying mathematical objects 'one prime at a time'.

Covers active learning, video lectures, exercises, categories, group actions, and abelian groups.

Explores divisibility and torsion in group theory, focusing on defining a functor that preserves divisibility.

Introduces subgroups and homomorphisms in group theory, with examples for illustration.

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

Focuses on demonstrating properties using Lemma 3.4 in group theory.

Covers abelian groups, Sylow subgroups, and variants on beta action.

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