Group Theory: The Center of a Group G is a Subgroup of G Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Group Theory: The Center of a Group G is a Subgroup of G Proof
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
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 26: Too many p groups
This video is part of an online mathematics course on group theory. We construct ridiculously large numbers of groups of order p^n, to explain why we do not try to classify them.
From playlist Group theory
The Special Linear Group is a Subgroup of the General Linear Group Proof
The Special Linear Group is a Subgroup of the General Linear Group Proof
From playlist Abstract Algebra
Groups of Prime Order p are Cyclic with p-1 Generators Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Groups of Prime Order p are Cyclic with p-1 Generators Proof. In this video we prove that if G is a finite group whose order is a prime number p, then G is cyclic and every non identity element is a generator. Since G has p-1 non id
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
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)
Visual Group Thoery, Lecture 5.5: p-groups
Visual Group Thoery, Lecture 5.5: p-groups Before we can introduce the Sylow theorems, we need to develop some theory about groups of prime power order, which we call p-groups. In this lecture, we show that the number of fixed point of a p-group acting on a set S is congruent modulo p to
From playlist Visual Group Theory
Group theory 24: Extra special groups
This lecture is part of an online mathematics course on group theory. It covers groups of order p^3. The non-abelian ones are examples of extra special groups, a sort of analog of the Heisenberg groups of quantum mechanics.
From playlist Group theory
GT20.1. Sylow Theorems - Proofs
Abstract Algebra: We give proofs of the three Sylow Theorems. Techniques include the class equation and group actions on subgroups. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-theory Master list at http://mathdoctorbob.org/UReddit.html
From playlist Abstract Algebra
Group theory 12: Cauchy's theorem
This lecture is part of an online mathematics course on group theory. It gives two proofs of Cauchy's theorem that if a prime p divides the order of a group then the group has an element of that order. It also uses Cauchy's theorem to classify the group of order 2p.
From playlist Group theory
Group theory 18: Nilpotent groups
This lecture is part of an online mathematics course on group theory. It lists the groups of order 16, and shows that a finite group is nilpotent if and only if it is a product of p-groups.
From playlist Group theory
Group theory 16: Automorphisms of cyclic groups
This lecture is part of an online mathematics course on group theory. It is mostly about the structure of the group of automorphisms of a cyclic group. As an application we classify the groups of order pq for primes p, q.
From playlist Group theory
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)
Group Theory for Physicists (Definitions with Examples)
In this video, we cover the most basic points that a physicist should know about group theory. Along the way, we'll give you lots of examples that illustrate each step. 00:00 Introduction 00:11 Definition of a Group 00:59 (1) Closure 01:34 (2) Associativity 02:02 (3) Identity Element 03:
From playlist Mathematical Physics
Visual Group Theory, Lecture 5.4: Fixed points and Cauchy's theorem
Visual Group Theory, Lecture 5.4: Fixed points and Cauchy's theorem We begin with a small lemma stating that if a group of prime order acts on a set S, then the number of fixed points is congruent to the size of the set, modulo p. We need this result to prove Cauchy's theorem, which says
From playlist Visual Group Theory