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Related lectures (31)

Subgroups and Cosets: Lagrange's Theorem

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

Group Presentation of S3

Covers the group presentation of S3, normal subgroups, generators, relations, quotient groups, and injective homomorphisms.

Amalgams: Group Pushouts

Covers the concept of amalgams, defining pushouts and quotient groups in group theory.

Group Theory: Quotients of Group

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

Applications of Lagrange's Theorem

Explores Lagrange's theorem applications in group theory and arithmetic, focusing on subgroups, cosets, quotient groups, and homomorphisms.

Group Homomorphisms: Kernels, Images, and Normal Subgroups

Explores group homomorphisms, kernels, images, and normal subgroups, using the dihedral group D_n as an example.

Applications of Lagrange's Theorem

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

Symmetric Group: Cycle Notation

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

Homogeneous Spaces and Quotients

Covers homogeneous spaces, group actions, and separating quotient spaces in mathematics.

Groupes quotient: Quotients de groupe

Explores quotient groups, left classes decomposition, group structure, and unique homomorphisms.

Abelianization of Fundamental Group

Explores abelianization examples, homomorphisms, and isomorphisms in group theory.

Subsets and subgroups associated with an action

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

Dihedral Group: Symmetries and Cosets

Explores the symmetries of a regular n-gon, normal subgroups, cosets, and Lagrange's theorem.

Isomorphism Theorems: Third Isomorphism Theorem

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

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.

Well Pointed Spaces and Wedge

Discusses well pointed spaces, neighborhoods, wedges, examples, and the universal property of the quotient.

Quotient Groups and Push-outs

Covers the construction of push-outs in the category Ens and philosophical concepts of universality and co-universality.

Groupes résolubles: Quotients and Subgroups

Explores the concept of solvable groups and their subgroups' impact on solvability.

Abélianization: Fundamental Groups

Explores abélianization of fundamental groups in commutative spaces with examples and proofs.

Resoluble Groups: Quotients of Group

Covers the definition of solvable groups and the abelian property of group quotients.

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