Group Theory: Introduction

Related lectures (32)

Explores group homomorphisms, emphasizing surjective mappings and their impact on group questions.

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

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

Explores symmetries in plane geometry, including isometries, reflections, and practical applications in design.

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

Explores the local structure of totally disconnected locally compact groups and their isomorphisms through conjugation.

Explores automorphism groups of trees and graphs, including actions on trees and group homomorphisms.

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

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Introduces the theory of abelian groups, focusing on p-abelian groups and their structure.

Explores Lagrange's theorem applications in group theory and arithmetic, focusing on subgroups, cosets, quotient groups, and homomorphisms.

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