Isomorphism: Order of Group Elements

Related lectures (29)

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Delves into advanced group theory concepts such as isomorphisms and homomorphisms.

Covers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.

Introduces adjunctions in Group Theory with examples of natural transformations and isomorphisms.

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

Explores the Monster group, a sporadic simple group with a unique representation theory.

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.

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

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

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