Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Concept

Presentation of a group

Related lectures (32)

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.

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.

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

Explores the impact of spatial configuration on teaching interactions in classrooms, analyzing seating arrangements and teacher movements.

Explores integer factorization using the quadratic sieve method and the challenges of working with algebraic number fields.

Covers the concept of homotopy classes and their properties in topology, including short components and group concatenation.

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

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

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.

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.