A group is (in a sense) the simplest structure in which we can do the familiar tasks associated with "algebra." First, in this video, we review the definition of a group.
From playlist Modern Algebra - Chapter 15 (groups)
Cyclic Groups (Abstract Algebra)
Cyclic groups are the building blocks of abelian groups. There are finite and infinite cyclic groups. In this video we will define cyclic groups, give a list of all cyclic groups, talk about the name “cyclic,” and see why they are so essential in abstract algebra. Be sure to subscribe s
From playlist Abstract Algebra
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin
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
Now that we know what a quotient group is, let's take a look at an example to cement our understanding of the concepts involved.
From playlist Abstract algebra
The idea of a quotient group follows easily from cosets and Lagrange's theorem. In this video, we start with a normal subgroup and develop the idea of a quotient group, by viewing each coset (together with the normal subgroup) as individual mathematical objects in a set. This set, under
From playlist Abstract algebra
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
Abstract Algebra | Group of Units modulo n
We sketch a proof that the equivalence classes of integers which are relatively prime to n form a group. This group is called the group of units modulo n. http://www.michael-penn.net
From playlist Abstract Algebra
Abstract Algebra: Motivation for the definition of a group
The definition of a group is very abstract. We motivate this definition with a simple, concrete example from basic algebra. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : https:/
From playlist Abstract Algebra
Lie Groups and Lie Algebras: Lesson 39 - The Universal Covering Group
Lie Groups and Lie Algebras: Lesson 39 - The Universal Covering Group We are finally in position to understand the nature of the Universal Covering Group and its connection to all the Lie groups which share a single Lie algebra. This is a critical lecture! In this lecture we simply state
From playlist Lie Groups and Lie Algebras
This lecture is part of an online graduate course on Lie groups. We give an introductory survey of Lie groups theory by describing some examples of Lie groups in low dimensions. Some recommended books: Lie algebras and Lie groups by Serre (anything by Serre is well worth reading) Repre
From playlist Lie groups
Why Are Prejudice and Conflict So Common? | Understanding the Mysteries of Human Behavior
It's no wonder discrimination seems to be everywhere: splitting people into two groups, even at random, makes them subconsciously dislike each other. A sense of competition can exaggerate these feelings. Pick up your tools; we've got some bridge building to do. Presented by Mark Leary Lea
From playlist Latest Uploads
Lie Groups and Lie Algebras: Lesson 38 - Preparation for the concept of a Universal Covering Group
Lie Groups and Lie Algebras: Lesson 38 - Preparation for the Universal Covering Group concept In this lesson we examine another amazing connection between the algebraic properties of the Lie groups with topological properties. We will lay the foundation to understand how discrete invaria
From playlist Lie Groups and Lie Algebras
Grothendieck Pairs and Profinite Rigidity - Martin Bridson
Arithmetic Groups Topic: Grothendieck Pairs and Profinite Rigidity Speaker: Martin Bridson Affiliation: Oxford University Date: January 26, 2022 If a monomorphism of abstract groups H↪G induces an isomorphism of profinite completions, then (G,H) is called a Grothendieck pair, recalling t
From playlist Mathematics
Regular permutation groups and Cayley graphs
Cheryl Praeger (University of Western Australia). Plenary Lecture from the 1st PRIMA Congress, 2009. Plenary Lecture 11. Abstract: Regular permutation groups are the 'smallest' transitive groups of permutations, and have been studied for more than a century. They occur, in particular, as
From playlist PRIMA2009
On the pioneering works of Professor I.B.S. Passi by Sugandha Maheshwari
PROGRAM GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fund
From playlist Group Algebras, Representations And Computation
Vincent Guirardel: Natural subgroups of automorphisms
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebra
Gilbert Levitt - Vertex finiteness for relatively hyperbolic groups
Gilbert Levitt (University of Caen, France) Given a finitely generated group G, we consider all splittings of G over subgroups in a fixed family (such as finite groups, cyclic groups, abelian groups). We discuss whether it is the case that only finitely many vertex groups appear, up to is
From playlist T1-2014 : Random walks and asymptopic geometry of groups.
Group actions on 1-manifolds: A list of very concrete open questions – Andrés Navas – ICM2018
Dynamical Systems and Ordinary Differential Equations Invited Lecture 9.8 Group actions on 1-manifolds: A list of very concrete open questions Andrés Navas Abstract: Over the last four decades, group actions on manifolds have deserved much attention by people coming from different fields
From playlist Dynamical Systems and ODE
Abstract Algebra | Cyclic Subgroups
We define the notion of a cyclic subgroup and give a few examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra