Universal Property of Groups

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Related lectures (30)

Group Theory Basics Log in to Mediaspace to watch this video

Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.

Untitled Log in to Mediaspace to watch this video

Quotients in Abelian Groups Log in to Mediaspace to watch this video

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 Homomorphisms Log in to Mediaspace to watch this video

Explores group homomorphisms, Euler's phi function, and group products.

Applications of Lagrange's Theorem Log in to Mediaspace to watch this video

Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.

Group Theory: Quotients of Group Log in to Mediaspace to watch this video

Covers normal subgroups, quotient groups, homomorphisms, and the categorical viewpoint in group theory.

Group Actions: Examples and Applications Log in to Mediaspace to watch this video

Explores examples of group actions on sets, emphasizing the utility of group actions to understand groups.

Subgroups and Cosets: Lagrange's Theorem Log in to Mediaspace to watch this video

Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.

Representation Theory: Algebras and Homomorphisms Log in to Mediaspace to watch this video

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Schur's Lemma and Representations Log in to Mediaspace to watch this video

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

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