In abstract algebra, the fundamental theorem on homomorphisms, also known as the fundamental homomorphism theorem, or the first isomorphism theorem, relates the structure of two objects between which a homomorphism is given, and of the kernel and image of the homomorphism. The homomorphism theorem is used to prove the isomorphism theorems. (Wikipedia).
Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
From playlist Abstract algebra
Homomorphisms in abstract algebra examples
Yesterday we took a look at the definition of a homomorphism. In today's lecture I want to show you a couple of example of homomorphisms. One example gives us a group, but I take the time to prove that it is a group just to remind ourselves of the properties of a group. In this video th
From playlist Abstract algebra
Group Homomorphisms and the big Homomorphism Theorem
This project was created with Explain Everything™ Interactive Whiteboard for iPad.
From playlist Modern Algebra
Chapter 6: Homomorphism and (first) isomorphism theorem | Essence of Group Theory
The isomorphism theorem is a very useful theorem when it comes to proving novel relationships in group theory, as well as proving something is a normal subgroup. But not many people can understand it intuitively and remember it just as a kind of algebraic coincidence. This video is about t
From playlist Essence of Group Theory
Now that we know what quotient groups, a kernel, and normal subgroups are, we can look at the first isomorphism theorem. It states that the quotient group created by the kernel of a homomorphism is isomorphic to the (second) group in the homomorphism.
From playlist Abstract algebra
Isomorphisms in abstract algebra
In this video I take a look at an example of a homomorphism that is both onto and one-to-one, i.e both surjective and injection, which makes it a bijection. Such a homomorphism is termed an isomorphism. Through the example, I review the construction of Cayley's tables for integers mod 4
From playlist Abstract algebra
Abstract Algebra | Group homomorphisms
We give a definition of group homomorphisms, some examples, and some general properties satisfied by these maps. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Visual Group Theory, Lecture 4.3: The fundamental homomorphism theorem
Visual Group Theory, Lecture 4.3: The fundamental homomorphism theorem The fundamental homomorphism theorem (FHT), also called the "first isomorphism theorem", says that the quotient of a domain by the kernel of a homomorphism is isomorphic to the image. We motivate this with Cayley diagr
From playlist Visual Group Theory
Group Isomorphisms in Abstract Algebra
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Group Isomorphisms in Abstract Algebra - Definition of a group isomorphism and isomorphic groups - Example of proving a function is an Isomorphism, showing the group of real numbers under addition is isomorphic to the group of posit
From playlist Abstract Algebra
Visual Group Theory, Lecture 4.5: The isomorphism theorems
Visual Group Theory, Lecture 4.5: The isomorphism theorems There are four central results in group theory that are collectively known at the isomorphism theorems. We introduced the first of these a few lectures back, under the name of the "fundamental homomorphism theorem." In this lectur
From playlist Visual Group Theory
On The Work Of Narasimhan and Seshadri (Lecture 3) by Edward Witten
Program Quantum Fields, Geometry and Representation Theory 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pandi
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Nursultan Kuanyshov: Lusternik-Schnirelmann category of group homomorphism
Nursultan Kuanyshov, University of Florida Title: Lusternik-Schnirelmann category of group homomorphism We prove the equality $\text{cat}(\phi)=\text{cd}(\phi)$ for homomorphisms $\phi:\Gamma\rightarrow \Lambda$ of a torsion free finitely generated nilpotent groups $\Gamma$ to an arbitrary
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Visual Group Theory, Lecture 7.3: Ring homomorphisms
Visual Group Theory, Lecture 7.3: Ring homomorphisms A ring homomorphism is a structure preserving map between rings, which means that f(x+y)=f(x)+f(y) and f(xy)=f(x)f(y) both must hold. The kernel is always a two-sided ideal. There are four isomorphism theorems for rings, which are compl
From playlist Visual Group Theory
Jordan Sahattchieve: A Fibering Theorem for 3-Manifolds
Jordan Sahattchieve Title: A Fibering Theorem for 3-Manifolds In this talk, I will endeavor to communicate a new fibering theorem for 3-manifolds in the style of Stalling's Fibration Theorem.
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Descent obstructions on constant curves over global (...) - Creutz - Workshop 2 - CEB T2 2019
Brendan Creutz (University of Canterbury) / 26.06.2019 Descent obstructions on constant curves over global function fields Let C and D be proper geometrically integral curves over a finite field and let K be the function field of D. I will discuss descent obstructions to the existence o
From playlist 2019 - T2 - Reinventing rational points
Dynamics on character varieties - William Goldman
Character Varieties, Dynamics and Arithmetic Topic: Dynamics on character varieties Speaker: William Goldman Affiliation: University of Maryland; Member, School of Mathematics Date: November 17, 2021 In these two talks, I will describe how the classification of locally homogeneous geomet
From playlist Mathematics
Alexander Dranishnikov (9/22/22): On the LS-category of group homomorphisms
In 50s Eilenberg and Ganea proved that the Lusternik-Schnirelmann category of a discrete group Γ equals its cohomological dimension, cat(Γ) = cd(Γ). We discuss a possibility of the similar equality cat(φ) = cd(φ) for group homomorphisms φ : Γ → Λ. We prove this equality for some classes of
From playlist Topological Complexity Seminar
What is a Group Homomorphism? Definition and Example (Abstract Algebra)
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys What is a Group Homomorphism? Definition and Example (Abstract Algebra)
From playlist Abstract Algebra