Group Theory Basics

Related lectures (30)

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

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Explores symmetries in physics through group theory, emphasizing how symmetries keep equations of motion unchanged.

Delves into group theory, emphasizing the centralizer of elements and the classification of finite abelian groups.

Introduces group theory concepts, including definitions and properties of groups, rings, and fields.

Covers the construction and universal properties of pushouts in group theory.

Explores isomorphism and the order of group elements, emphasizing matching identities and inverses.

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Explores the construction of the Fischer-Greiss monster group, emphasizing its key properties and the process involved.