Combinatorial Group Theory

Related lectures (55)

Explores group actions, defining functors on groups, and verifying properties of group actions.

Covers subgroups, generators, cyclic groups, and group morphisms in group theory.

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

Explores examples of group actions on sets, emphasizing the utility of group actions to understand groups.

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

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

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

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

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

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

Explores the concept of p-subgroups of Sylow in group theory, emphasizing the philosophy of studying mathematical objects 'one prime at a time'.

Explores solvable groups, group actions, normalizers, and stabilizers in group theory.

Focuses on abelian p-groups, demonstrating technical results for classifying finite abelian groups.

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

Covers the criteria for subgroups and provides examples and proofs.

Explores the Hom functor for abelian groups and its relation to direct sums.

Explores the concept of fractions of rings and their uniqueness in ideals and quotients.

Covers group quotient, group actions, and functors connecting sets and G-sets.

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

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