Applications of Lagrange's Theorem

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Page 2 of 3

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

Introduces normal subgroups, group quotients, and their applications in group theory.

Delves into push-out and quotients in group theory, emphasizing homomorphisms and normal subgroups.

Explores the third isomorphism theorem in group theory, focusing on quotient groups and a categorical perspective.

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

Explores group homomorphisms, constructing isomorphisms between groups using generators and relations.

Covers normal subgroups, quotient groups, homomorphisms, and the categorical viewpoint in group theory.

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

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

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