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Torsion: Hom Functoriality and Exact Sequences
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Abelian Groups: Free Abelian Groups
Explores free abelian groups, homomorphisms, and exact sequences in group theory.
Active Learning: Group Theory
Explores adjoint functors, points fixes, orbits, and non-trivial actions in group theory.
Torsion and Divisibility in Group Theory
Explores the relationship between p-torsion and p-divisibility in group theory, highlighting implications of p-divisibility in exact sequences of abelian groups.
Group Direct Sums in Group Theory
Explores direct sums in group theory, focusing on abelian groups and their implications.
Free Abelian Groups: Group Theory
Explores the concept of free abelian groups as an important left adjoint functor.
Finitely Generated Abelian Groups
Explores finitely generated abelian groups, focusing on their structure and isomorphism theorems.
Resoluble Groups: Quotients of Group
Covers the definition of solvable groups and the abelian property of group quotients.
Sylow Subgroups: Group Theory
Explores the concept of p-subgroups of Sylow in group theory, emphasizing the philosophy of studying mathematical objects 'one prime at a time'.
Natural Transformations: Functors and Categories
Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.
Torsion and Divisibility: Abelian Groups
Introduces torsion and divisibility concepts in abelian groups to describe their structure.
