Hom Functor: Abelian Groups

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Related lectures (54)

Group Operations and Homomorphisms in Abelian Groups Log in to Mediaspace to watch this video

Explores operations on abelian groups, Homomorphisms, adjoints, and morphisms in group theory.

Groups: Definitions, Properties, and Homomorphisms Log in to Mediaspace to watch this video

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.

Representation Theory: Algebras and Homomorphisms Log in to Mediaspace to watch this video

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Direct Sums of Abelian Groups Log in to Mediaspace to watch this video

Covers direct sums of abelian groups, group actions, and vector spaces, including coproducts and homomorphisms.

Direct Sums Arithmetic Log in to Mediaspace to watch this video

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

Group Theory: Direct Sum of Abelian Groups Log in to Mediaspace to watch this video

Explores the arithmetic of direct sum of abelian groups and the process of turning a monoid into a commutative group.

Algebra: Group Actions and Direct Products Log in to Mediaspace to watch this video

Covers group actions, conjugacy classes, centralizers, direct products, and finite abelian groups.

Direct Products in Group Theory Log in to Mediaspace to watch this video

Explores direct products in group theory, including semi-direct products and group properties.

Torsion: Hom Functoriality and Exact Sequences Log in to Mediaspace to watch this video

Explores the concept of torsion in group theory, focusing on its Hom functoriality and its role in exact sequences.

Sylow Subgroups: Structure and Properties Log in to Mediaspace to watch this video

Explores the properties and structure of Sylow subgroups in group theory, emphasizing a theorem-independent approach.

Group Actions: Equivariance and Functors Log in to Mediaspace to watch this video

Explores equivariance in group actions and functors, demonstrating its importance in group theory.

Functors and Homomorphisms in Group Theory Log in to Mediaspace to watch this video

Explores functors F_{Ab} and Hom (-,-) in group theory, including presentations and homomorphisms.

Applications of Lagrange's Theorem Log in to Mediaspace to watch this video

Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.

Sylow Subgroups: Group Theory Log in to Mediaspace to watch this video

Explores the concept of p-subgroups of Sylow in group theory, emphasizing the philosophy of studying mathematical objects 'one prime at a time'.

Symmetric Group: Cycle Notation Log in to Mediaspace to watch this video

Explores the symmetric group, emphasizing cycle notation and group properties.

Finitely Generated Abelian Groups Log in to Mediaspace to watch this video

Explores finitely generated abelian groups, focusing on their structure and isomorphism theorems.

Group Theory: Active Learning Session Log in to Mediaspace to watch this video

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

Group Theory Basics Log in to Mediaspace to watch this video

Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.

Abelian p-groups: Groupes abéliens Log in to Mediaspace to watch this video

Focuses on abelian p-groups, demonstrating technical results for classifying finite abelian groups.

Quotient Groups: Homomorphisms and Isomorphisms Log in to Mediaspace to watch this video

Explores quotient groups, homomorphisms, isomorphisms, and push-outs in different categories.

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