Connected Components

Related lectures (31)

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

Explores permutations preserving adjacency, linear transformations, groups, and sub-groups.

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

Covers the role of symmetries and groups in quantum mechanics, focusing on SU2 and SU3, their properties, and implications for physical theories.

Introduces characters as group homomorphisms from linear algebraic groups to multiplicative groups.

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

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

Explores the torus, linear groups, stability properties of matrices, and homomorphisms.

Explores automorphism groups of trees and graphs, including actions on trees and group homomorphisms.