Lectures related to Presentation of a group

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

Introduces combinatorial group theory, emphasizing group presentations, normal subgroups, and group quotients.

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

Covers the concept of group presentations using generators and relations to define groups.

Covers the concept of the free product in group theory and how to determine monomorphisms and homomorphisms.

Covers Euler's totient function, group theory, homomorphisms, and group isomorphisms.

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

Delves into homotopy identification, pushout diagrams, colimits, and group fundamental calculations.

Covers exact sequences, torsion, divisibility, and operations on abelian groups.

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

Covers group theory with a focus on group presentations and subgroup generation.

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

Demonstrates the existence of p-Sylow subgroups in any finite group using induction and the abelian case.

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

Explores abelian groups from a categorical perspective, discussing the coproduct construction.

Explores the properties of p-subgroups of Sylow in a group.

Covers the concept of algebraic quotients in the context of a-variety.

Explores the concept of direct sums in abelian groups, emphasizing the universal property and homomorphisms.

Explores the definition of orbits and fixed points of a G-object in any category, focusing on G-equivariant applications.

Covers the fundamental theorem of finitely generated modules over a PID.