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Related lectures (32)
Group Theory Basics: Subgroups and Homomorphisms
Introduces subgroups and homomorphisms in group theory, with examples for illustration.
Automorphism Groups: Trees and Graphs III
Explores automorphism groups of trees and graphs, including actions on trees and group homomorphisms.
Fundamental Groups
Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Endomorphisms and automorphisms of totally disconnected locally compact groups I
Covers the definitions and basic results of endomorphisms and automorphisms of totally disconnected locally compact groups.
Push-out and Quotients
Delves into push-out and quotients in group theory, emphasizing homomorphisms and normal subgroups.
Group Actions: G-object Notion
Explores the categorical framework for group actions, focusing on the concept of G-objects in different categories.
Normal Subgroups and Quotients
Introduces normal subgroups, group quotients, and their applications in group theory.
Recap of Group Theory
Provides a recap of group theory, defining a group as a set with a multiplication operation.
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.
Local structure of totally disconnected locally compact groups I
Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.
Cohomology: Cross Product
Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.
Group Cohomology
Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
Self-similar groups: Automorphisms of rooted trees
Covers self-similar groups and automorphisms of rooted trees, exploring residually finite groups and congruence subgroups.
Group Theory Basics
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Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.
RSA Encryption: Main Concepts
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Covers the main concepts behind RSA encryption and examples of homomorphisms between cyclic 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.
Universal Property of Groups
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Explores the universal property of groups, defining homomorphisms and exploring subgroup properties.
Group Morphisms: Injectivity and Conjugation
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Explores group morphisms, injectivity criteria, and conjugation concepts within groups.
Group Homomorphisms
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Explores group homomorphisms, Euler's phi function, and group products.
Categorical Perspective: Group Quotients
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Explores the categorical sense of constructing a group quotient by a normal subgroup, showing it as a specific example of a more general construction.
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