Group extension

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

Group theory 8: Extensions

This is lecture 8 of an online mathematics course on group theory. It discusses extensions of groups and uses them to classify the five groups of order 8.

From playlist Group theory

What is Group Theory?

This video contains the origins of group theory, the formal definition, and theoretical and real-world examples for those beginning in group theory or wanting a refresher :)

From playlist Summer of Math Exposition Youtube Videos

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

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

GT2. Definition of Subgroup

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

301.2 Definition of a Group

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)

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

Group Theory I Introduction

A set and a binary operation will form a group if four conditions are satisfied. We take a look at the conditions of closure, associativity, identity and inverse.

From playlist Foundational Math

Galois theory: Infinite Galois extensions

This lecture is part of an online graduate course on Galois theory. We show how to extend Galois theory to infinite Galois extensions. The main difference is that the Galois group has a topology, and intermediate field extensions now correspond to closed subgroups of the Galois group. We

From playlist Galois theory

Lecture 35. Galois extensions and the Main Theorem

From playlist Abstract Algebra 2

CTNT 2020 - Infinite Galois Theory (by Keith Conrad) - Lecture 3

The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2020 - Infinite Galois Theory (by Keith Conrad)

CTNT 2020 - Infinite Galois Theory (by Keith Conrad) - Lecture 4

The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2020 - Infinite Galois Theory (by Keith Conrad)

Visual Group Theory, Lecture 6.5: Galois group actions and normal field extensions

Visual Group Theory, Lecture 6.5: Galois group actions and normal field extensions If f(x) has a root in an extension field F of Q, then any automorphism of F permutes the roots of f(x). This means that there is a group action of Gal(f(x)) on the roots of f(x), and this action has only on

From playlist Visual Group Theory

CTNT 2022 - Local Fields (Lecture 4) - by Christelle Vincent

This video is part of a mini-course on "Local Fields" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2022 - Local Fields (by Christelle Vincent)

CTNT 2020 - Iwasawa Theory of Fine Selmer Groups - Debanjana Kundu

The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2020 - Conference Videos

CTNT 2020 - Infinite Galois Theory (by Keith Conrad) - Lecture 1

The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2020 - Infinite Galois Theory (by Keith Conrad)

Kevin Buzzard (lecture 3/20) Automorphic Forms And The Langlands Program [2017]

Full course playlist: https://www.youtube.com/playlist?list=PLhsb6tmzSpiysoRR0bZozub-MM0k3mdFR http://wwwf.imperial.ac.uk/~buzzard/MSRI/ Summer Graduate School Automorphic Forms and the Langlands Program July 24, 2017 - August 04, 2017 Kevin Buzzard (Imperial College, London) https://w

From playlist MSRI Summer School: Automorphic Forms And The Langlands Program, by Kevin Buzzard [2017]

Galois theory: Galois extensions

This lecture is part of an online graduate course on Galois theory. We define Galois extensions in 5 different ways, and show that 4 f these conditions are equivalent. (The 5th equivalence will be proved in a later lecture.) We use this to show that any finite group is the Galois group of

From playlist Galois theory

Subgroups 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