Now that we have defined and understand quotient groups, we need to look at product groups. In this video I define the product of two groups as well as the group operation, proving that it is indeed a group.
From playlist Abstract algebra
There is no better way of understanding product groups than working through and example. In this video we look at the product group of the cyclic group with two elements and itself. The final result is isomorphic to what we call the Klein 4 group.
From playlist Abstract algebra
Definition of a group Lesson 24
In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el
From playlist Abstract algebra
This video defines and give the notation used for subsets and proper subsets. http://mathispower4u.com
From playlist Sets
Definition of a Subgroup in Abstract Algebra with Examples of Subgroups
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Subgroup in Abstract Algebra with Examples of Subgroups
From playlist Abstract Algebra
Abstract Algebra: We define the notion of a subgroup and provide various examples. We also consider cyclic subgroups and subgroups generated by subsets in a given group G. Example include A4 and D8. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-
From playlist Abstract Algebra
Group theory 7: Semidirect products
This is lecture 7 of an online course on group theory. It covers semidirect products and uses them to classify groups of order 6.
From playlist Group theory
What is a Group? | Abstract Algebra
Welcome to group theory! In today's lesson we'll be going over the definition of a group. We'll see the four group axioms in action with some examples, and some non-examples as well which violate the axioms and are thus not groups. In a fundamental way, groups are structures built from s
From playlist Abstract Algebra
In this tutorial we define a subgroup and prove two theorem that help us identify a subgroup. These proofs are simple to understand. There are also two examples of subgroups.
From playlist Abstract algebra
8ECM Invited Lecture: Aner Shalev
From playlist 8ECM Invited Lectures
The Math You Didn't Learn | #SoME2
Sometimes people wonder what actual mathematicians do. Do they crunch large numbers? Participate in competitions with each other? (They actually did a lot of that in the Middle Ages). Are they geniuses whose activites are unfathomable for us normal people? Math is a very large field, but m
From playlist Summer of Math Exposition 2 videos
Stable and NIP regularity in groups - G. Conant - Workshop 1 - CEB T1 2018
Gabriel Conant (Notre Dame) / 01.02.2018 We use local stability theory to prove a group version of Szemer´edi regularity for stable subsets of finite groups. Toward generalizing this result to the NIP setting, we consider definable set systems of finite VC-dimension in pseudofinite groups
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Hankyung Ko: A singular Coxeter presentation
SMRI Algebra and Geometry Online Hankyung Ko (Uppsala University) Abstract: A Coxeter system is a presentation of a group by generators and a specific form of relations, namely the braid relations and the reflection relations. The Coxeter presentation leads to, among others, a similar pre
From playlist SMRI Algebra and Geometry Online
Plenary lecture 2 by Emmanuel Breuillard - Part 1
Geometry Topology and Dynamics in Negative Curvature URL: https://www.icts.res.in/program/gtdnc DATES: Monday 02 Aug, 2010 - Saturday 07 Aug, 2010 VENUE : Raman Research Institute, Bangalore DESCRIPTION: This is An ICM Satellite Conference. The conference intends to bring together ma
From playlist Geometry Topology and Dynamics in Negative Curvature
First-order rigidity, bi-interpretability, and congruence subgroups - Nir Avni
Arithmetic Groups Topic: First-order rigidity, bi-interpretability, and congruence subgroups Speaker: Nir Avni Affiliation: Northwestern University Date: October 13, 2021 I'll describe a method for analyzing the first-order theory of an arithmetic group using its congruence quotients. W
From playlist Mathematics
Introduction to additive combinatorics lecture 1.0 --- What is additive combinatorics?
This is an introductory video to a 16-hour course on additive combinatorics given as part of Cambridge's Part III mathematics course in the academic year 2021-2. After a few remarks about practicalities, I informally discuss a few open problems, and attempt to explain what additive combina
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Pseudo-finite dimensions, modularity, and generalisations (...) - M. Bays - Workshop 1 - CEB T1 2018
Martin Bays (Münster) / 29.01.2018 Pseudo-finite dimensions, modularity, and generalisations of Elekes–Szab´o. Given a system of polynomial equations in m complex variables with solution set V of dimension d, if we take finite subsets Xi of C each of size N, then the number of solutions
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Centralizer of a set in a group
A centralizer consider a subset of the set that constitutes a group and included all the elements in the group that commute with the elements in the subset. That's a mouthful, but in reality, it is actually an easy concept. In this video I also prove that the centralizer of a set in a gr
From playlist Abstract algebra
God's Binomial Identity. #SoME2
My submission for SoME2. Please support my research https://paypal.me/feralmathematician?locale.x=en_US
From playlist Summer of Math Exposition 2 videos