Simple Groups - Abstract Algebra
Simple groups are the building blocks of finite groups. After decades of hard work, mathematicians have finally classified all finite simple groups. Today we talk about why simple groups are so important, and then cover the four main classes of simple groups: cyclic groups of prime order
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
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)
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
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
Chapter 5: Quotient groups | Essence of Group Theory
Quotient groups is a very important concept in group theory, because it has paramount importance in group homomorphisms (connection with the isomorphism theorem(s)). With this video series, abstract algebra needs not be abstract - one can easily develop intuitions for group theory! In fac
From playlist Essence of Group Theory
Groups in abstract algebra examples
In this tutorial I discuss two more examples of groups. The first contains four elements and they are the four fourth roots of 1. The second contains only three elements and they are the three cube roots of 1. Under the binary operation of multiplication, these sets are in fact groups.
From playlist Abstract algebra
This lecture is part of an online math course on group theory. We review free abelian groups, then construct free (non-abelian) groups, and show that they are given by the set of reduced words, and as a bonus find that they are residually finite.
From playlist Group theory
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
8ECM Invited Lecture: Aner Shalev
From playlist 8ECM Invited Lectures
Generic semistability of representations of reductive groups by Donghoon David Hyeon
Algebraic Surfaces and Related Topics PROGRAM URL : http://www.icts.res.in/program/AS2015 DESCRIPTION : This is a joint program of ICTS with TIFR, Mumbai and KIAS, Seoul. The theory of surfaces has been the cradle to many powerful ideas in Algebraic Geometry. The problems in this area
From playlist Algebraic Surfaces and Related Topics
Definably simple groups in valued fields - D. Macpherson - Workshop 3 - CEB T1 2018
Dugald Macpherson (Leeds) / 29.03.2018 D-varieties and the Dixmier-Moeglin Equivalence About four years ago, a new application of the model theory of differentially closed fields arose. The target was the Dixmier-Moeglin equivalence problem (DME) in noncommutative affine algebras, as wel
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Bettina EICK - Computational group theory, cohomology of groups and topological methods 5
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computation
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
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
Measure Growth in Compact Simple Lie Groups - Yifan Jing
Special Year Research Seminar Topic: Measure Growth in Compact Simple Lie Groups Speaker: Yifan Jing Affiliation: University of Oxford Date: November 08, 2022 The celebrated product theorem says if A is a generating subset of a finite simple group of Lie type G, then |AAA| \gg \min \{ |A
From playlist Mathematics
Structure of group rings and the group of units of integral group rings (Lecture 2) by Eric Jespers
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 fun
From playlist Group Algebras, Representations And Computation
Intrinsic Diophantine approximation (Lecture 2) by Amos Nevo
PROGRAM SMOOTH AND HOMOGENEOUS DYNAMICS ORGANIZERS: Anish Ghosh, Stefano Luzzatto and Marcelo Viana DATE: 23 September 2019 to 04 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases.
From playlist Smooth And Homogeneous Dynamics
[BOURBAKI 2018] 13/01/2018 - 2/4 - Raphaël BEUZART-PLESSIS
Progrès récents sur les conjectures de Gan-Gross-Prasad [d'après Jacquet-Rallis, Waldspurger, W. Zhang, etc.] Les conjectures de Gan-Gross-Prasad ont deux aspects: localement elles décrivent de façon explicite certaines lois de branchements entre représentations de groupes de Lie réels ou
From playlist BOURBAKI - 2018
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
Proper Actions and Representation Theory Part 3
Professor Toshiyuki Kobayashi, University of Tokyo, Japan
From playlist Distinguished Visitors Lecture Series