Homomorphisms and Isomorphisms

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (57)

Two Definitions of Group Action Log in to Mediaspace to watch this video

Explores two definitions of group action on a set, focusing on properties and applications.

Group Homomorphisms Log in to Mediaspace to watch this video

Explores group homomorphisms, Euler's phi function, and group products.

Groups: Definitions, Properties, and Homomorphisms Log in to Mediaspace to watch this video

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.

Group Homomorphisms Log in to Mediaspace to watch this video

Explores group homomorphisms, isomorphisms, and generators in abstract algebra.

Quotient Groups: Homomorphisms and Isomorphisms Log in to Mediaspace to watch this video

Explores quotient groups, homomorphisms, isomorphisms, and push-outs in different categories.

Subrepresentations of the regular representation Log in to Mediaspace to watch this video

Explores subrepresentations of the regular representation in group theory, emphasizing properties and isomorphism between subrepresentations.

Direct Sums: Abelian Groups Log in to Mediaspace to watch this video

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

RSA Encryption: Main Concepts Log in to Mediaspace to watch this video

Covers the main concepts behind RSA encryption and examples of homomorphisms between cyclic groups.

Isomorphism Theorems: Quotients of Group Log in to Mediaspace to watch this video

Explores the isomorphism theorems for quotient groups and the concept of surjective homomorphisms.

Group Actions: Theory and Examples Log in to Mediaspace to watch this video

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

Abelian Groups: Free Abelian Groups Log in to Mediaspace to watch this video

Explores free abelian groups, homomorphisms, and exact sequences in group theory.

Homomorphism of Groups: Signature Log in to Mediaspace to watch this video

Explores homomorphisms of groups, focusing on the signature sgn and the concept of cycles and transpositions.

The Lemma of the Five: Abelian Groups Log in to Mediaspace to watch this video

Presents the Lemma of the Five, a fundamental result in group theory.

Representation Theory: Algebras and Homomorphisms Log in to Mediaspace to watch this video

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Class Equation and Burnside's Lemma Log in to Mediaspace to watch this video

Explores the class equation and Burnside's lemma in group theory.

Lagrange's Theorem: Applications and Homomorphisms Log in to Mediaspace to watch this video

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

Groupes Isomorphes: Applications Log in to Mediaspace to watch this video

Explores isomorphic groups, bijective morphisms, and their applications in group theory.

Principal Ideal Domains: Structure and Homomorphisms Log in to Mediaspace to watch this video

Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.

Linear Transformations: Kernels and Images Log in to Mediaspace to watch this video

Covers kernels and images of linear transformations between vector spaces.

Linear Maps and Bases: The Rank Theorem Log in to Mediaspace to watch this video

Covers bijective linear maps, invertibility of matrices, isomorphisms, and the rank theorem.

Page 2 of 3