Subgroups and Cosets: Lagrange's Theorem

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Universal Property of Groups

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

Group Theory Basics

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

Subsets and subgroups associated with an action

Explores subsets, subgroups, actions, fixed points, stabilizers, orbits, and bijections in group theory.

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.

Group Theory: Quotients of Group

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

Lagrange's Theorem: Applications and Homomorphisms

Covers Lagrange's theorem, group homomorphisms, congruence classes, and normal subgroups.

Proper Actions and Quotients

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Mathematical Parenthesis on Groups and Lagrange Theorem

Explores cosets in commutative groups, Lagrange theorem, and integer factorization.

Topology: Free Groups and Their Properties

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

Categorical Perspective: Group Quotients

Explores the categorical sense of constructing a group quotient by a normal subgroup, showing it as a specific example of a more general construction.