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Related lectures (32)

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

Explores concrete examples of group actions on sets, focusing on actions that do not change the set.

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Group Theory Basics Log in to Mediaspace to watch this video

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

Universal Property of Groups Log in to Mediaspace to watch this video

Explores the universal property of groups, defining homomorphisms and exploring subgroup properties.

Categorical Perspective: Abelian Groups Log in to Mediaspace to watch this video

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

Morphism of Groups Log in to Mediaspace to watch this video

Covers the concept of morphism of groups, actions on sets, and automorphisms.

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.

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.

Groups and Homomorphisms Log in to Mediaspace to watch this video

Covers Euler's totient function, group theory, homomorphisms, and group isomorphisms.

Invariant Definitions Log in to Mediaspace to watch this video

Explores invariant definitions in sets, groups, and automorphisms, including p-divisible groups and free abelian groups.

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

Explores Lagrange's theorem applications in group theory and arithmetic, focusing on subgroups, cosets, quotient groups, and homomorphisms.

Elliptic Curves: Group Structure and Isomorphism Log in to Mediaspace to watch this video

Explores the group structure and isomorphism of elliptic curves, including inverses, associativity, and compactification to the torus.

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