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Lecture
Torsion and Divisibility: Abelian Groups
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Related lectures (31)
Categorical Perspective: Abelian Groups
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Explores abelian groups from a categorical perspective, discussing the coproduct construction.
Group Operations and Quotients
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Explores group operations with cyclic properties and the universal ownership of quotients.
Abelian p-groups: Groupes abéliens
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Focuses on abelian p-groups, demonstrating technical results for classifying finite abelian groups.
Group Presentations: Abelian Groups
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Covers exact sequences, torsion, divisibility, and operations on abelian groups.
Algebra: Practice Exam Solutions
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Covers the solution of a practice exam in Algebra, focusing on finding greatest common divisors of polynomials and exploring group properties.
Subgroups and Cosets: Lagrange's Theorem
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Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.
Hom Functor: Abelian Groups
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Explores the Hom functor for abelian groups and its relation to direct sums.
Quotients in Abelian Groups
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Covers quotients in abelian groups and the concept of free abelian groups, showing that every abelian group is isomorphic to a quotient of a free abelian group.
Group Theory Basics
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Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.
The Lemma of the Five: Abelian Groups
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Presents the Lemma of the Five, a fundamental result in group theory.
Group Direct Sums in Group Theory
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Explores direct sums in group theory, focusing on abelian groups and their implications.
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