Subgroups and Generators

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Related lectures (33)

Categorical Perspective: Group Quotients Log in to Mediaspace to watch this video

Explores the categorical sense of constructing a group quotient by a normal subgroup, showing it as a specific example of a more general construction.

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.

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

Explores group actions, defining functors on groups, and verifying properties of group actions.

Direct Sums Arithmetic Log in to Mediaspace to watch this video

Explores the arithmetic of direct sums in group theory, discussing conditions for equality.

Subsets and subgroups associated with an action Log in to Mediaspace to watch this video

Explores subsets, subgroups, actions, fixed points, stabilizers, orbits, and bijections in group theory.

Torsion and Divisibility: Abelian Groups Log in to Mediaspace to watch this video

Introduces torsion and divisibility concepts in abelian groups to describe their structure.

Groups & Rings: Morphisms, Kernels, and Injectivity Log in to Mediaspace to watch this video

Explores group morphisms, kernels, and injectivity in group theory.

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.

Centralizer, normalizer, and center Log in to Mediaspace to watch this video

Covers the concepts of normalizer, centralizer, and center in group theory, providing examples of their applications.

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.

Groups & Subgroups: Definitions, Theorems, and Morphisms Log in to Mediaspace to watch this video

Covers the fundamental concepts of groups and subgroups, including definitions, theorems, and morphisms.

Group Theory Fundamentals Log in to Mediaspace to watch this video

Introduces group theory basics and group action concepts with associated subsets.

Dihedral Group: Symmetries and Cosets Log in to Mediaspace to watch this video

Explores the symmetries of a regular n-gon, normal subgroups, cosets, and Lagrange's theorem.

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