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Group Theory Basics
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Related lectures (51)
Recap of Group Theory
Provides a recap of group theory, defining a group as a set with a multiplication operation.
Fundamental Groups
Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Group Theory Basics
Covers the fundamental concepts of group theory and examples of real numbers and permutations.
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Local structure of totally disconnected locally compact groups I
Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.
Push-out and Quotients
Delves into push-out and quotients in group theory, emphasizing homomorphisms and normal subgroups.
Topology: Free Groups and Their Properties
Discusses the theory of free groups, their properties, and relationships with other algebraic structures.
Isometries and Group Homomorphisms
Explores isometries, group homomorphisms, linear transformations, and group generation by similarities.
Endomorphisms and automorphisms of totally disconnected locally compact groups V
Explores endomorphisms and automorphisms of totally disconnected locally compact groups, emphasizing surjective homomorphisms and free abelian groups.
Groups: Definitions, Properties, and Homomorphisms
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Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.
Groups and Products
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Covers the concepts of groups, products, and homomorphisms, focusing on the hx set and group alternates.
Group Actions: Examples and Applications
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Explores examples of group actions on sets, emphasizing the utility of group actions to understand groups.
Universal Property of Groups
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Explores the universal property of groups, defining homomorphisms and exploring subgroup properties.
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Morphism of Groups
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Covers the concept of morphism of groups, actions on sets, and automorphisms.
Applications of Lagrange's Theorem
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Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.
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Groups & Rings: Morphisms, Kernels, and Injectivity
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Explores group morphisms, kernels, and injectivity in group theory.
Two Definitions of Group Action
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Explores two definitions of group action on a set, focusing on properties and applications.
Symmetric Group: Cycle Notation
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Explores the symmetric group, emphasizing cycle notation and group properties.
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