Torsion and Divisibility

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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.

Abelian Groups: First Approach

Introduces the theory of abelian groups, focusing on p-abelian groups and their structure.

Existence: Proof of Classification Theorem

Covers the proof of the Classification Theorem for finite abelian groups, demonstrating the existence of a decomposition into cyclic groups.

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 Theory: Active Learning Session

Delves into group theory, emphasizing the centralizer of elements and the classification of finite abelian groups.

Algebra Review: Rings, Fields, and Groups

Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.

Algebra: Practice Exam Solutions

Covers the solution of a practice exam in Algebra, focusing on finding greatest common divisors of polynomials and exploring group properties.

Abelian Groups: Technical Lemmas

Covers technical lemmas on abelian p-groups and maximal order elements.

Existence in Abelian Case and Group Center

Explores the existence of p-Sylow subgroups in finite groups and the abelian group center.

Abelian Groups: Fourth Property

Explores the fourth property of p-Sylow subgroups in abelian groups.