Finite Abelian Groups

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (30)

Page 2 of 3

Categorical Perspective: Abelian Groups

Explores abelian groups from a categorical perspective, discussing the coproduct construction.

Direct Sum of Subgroups

Explores the direct sum of subgroups in an abelian group and introduces the coproduct concept in Abelian categories.

Classification of Finite Abelian Groups

Covers the classification of finite abelian groups and the unique sequence of positive integers for isomorphism.

Groups: Definitions, Properties, and Homomorphisms

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

Subgroups and Cosets: Lagrange's Theorem

Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.

Untitled

Classification of Finite Abelian Groups

Covers the classification theorem for finite abelian groups and introduces rings, including zero divisors and domains.

Group Algebra: Maschke's Theorem

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Existence of Direct Sums: Abelian Groups

Demonstrates the existence of direct sums of abelian groups and covers propositions and proofs related to their uniqueness.

Applications of Lagrange's Theorem

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