Torsion and Divisibility

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

Covers exact sequences, torsion, divisibility, and operations on abelian groups.

Explores invariant definitions in sets, groups, and automorphisms, including p-divisible groups and free abelian groups.

Focuses on abelian p-groups, demonstrating technical results for classifying finite abelian groups.

Explores the classification of finite abelian groups and rings, emphasizing elementary divisors and properties of rings.

Covers useful lemmas for p-groups, including divisibility properties and the existence of specific elements in finite abelian groups.

Introduces torsion and divisibility concepts in abelian groups to describe their structure.

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

Explores exact sequences of abelian group homomorphisms and provides examples.