Introduction to Group Theory

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Related lectures (31)

The Lemma of the Five: Abelian Groups

Presents the Lemma of the Five, a fundamental result in group theory.

Group Direct Sums in Group Theory

Explores direct sums in group theory, focusing on abelian groups and their implications.

Abelian p-groups: Groupes abéliens

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

Free Abelian Groups: Group Theory

Explores the concept of free abelian groups as an important left adjoint functor.

Abelian Groups: First Approach

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

Group Theory: Direct Sum of Abelian Groups

Explores the arithmetic of direct sum of abelian groups and the process of turning a monoid into a commutative group.

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.

Abelian Groups: Free Abelian Groups

Explores free abelian groups, homomorphisms, and exact sequences in group theory.

Finite Abelian Groups: Classification Theorem

Presents the classification of finite abelian groups as products of cyclic groups, a fundamental result in various branches of mathematics.

Quasi-Categories: Active Learning Session

Covers fibrant objects, lift of horns, and the adjunction between quasi-categories and Kan complexes, as well as the generalization of categories and Kan complexes.

Group Actions: Equivariance and Functors

Explores equivariance in group actions and functors, demonstrating its importance in group theory.

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