Group Theory: Subsets and Lagrange Theorem

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

Introduces subgroups and homomorphisms in group theory, with examples for illustration.

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

Provides a recap of group theory, defining a group as a set with a multiplication operation.

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Explores two definitions of group action on a set, focusing on properties and applications.

Explores quotients of groups by equivalence relations and the conditions for well-defined sets.

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

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