Algebra: Group Actions and Direct Products

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Description

This lecture covers the action of a group on itself by conjugations, conjugacy classes, centralizers, and the class equation of a finite group. It also discusses the direct product of groups, including basic properties and the classification of finite abelian groups.

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Mathematics

Algebra: Representation theory, Abstract algebra

Related lectures (30)

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In course

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Instructor

aute cillum

Ontological neighbourhood

Mathematics

Algebra: Representation theory, Abstract algebra

Related lectures (30)

Orbit-Stabilizer Theorem: Conjugacy Classes and Direct Products

Covers the Orbit-Stabilizer theorem, conjugacy classes, and direct products in finite groups.

Untitled

Conjugation in Groups

Explores conjugation in groups, the direct product of groups, and the classification of finite abelian groups.

Proper Actions and Quotients

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Categorical Perspective: Abelian Groups

Explores abelian groups from a categorical perspective, discussing the coproduct construction.