Lectures related to Examples of groups

Explores small order groups, group morphisms, and the second isomorphism theorem.

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

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

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

Explores Coxeter groups, emphasizing generators, relations, and unique presentations in group theory.

Explores group morphisms, injectivity criteria, and conjugation concepts within groups.

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

Explores concrete examples of group actions on sets, focusing on actions that do not change the set.

Covers the concept of morphism of groups, actions on sets, and automorphisms.

Covers the concept of the renormalization group and the effective Hamiltonian.

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

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

Delves into the symmetries of regular polygons, including the dihedral group and left cosets in a finite group.

Covers the solution of a practice exam in Algebra, focusing on finding greatest common divisors of polynomials and exploring group properties.

Explores regular homomorphisms and unipotent elements in group theory.

Explores algebraic structures, classes of examples, and properties of cyclic groups.

Explores symmetry in chemistry, covering reflection planes, dihedral groups, cubic groups, and geometric shapes.

Covers the criteria for subgroups and provides examples and proofs.

Covers the definition and properties of the scalar product, including geometric interpretations and algebraic properties.

Explores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.