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
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 | 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
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
Abstract Algebra | The center of a group.
We give the definition of the center of a group, prove that it is a subgroup, and give an example. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
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
Group theory 6: normal subgroups and quotient groups
This is lecture 6 of an online mathematics course on groups theory. It defines normal subgroups and quotient groups, using the non-abelian group of order 6 as an example.
From playlist Group theory
This is lecture 5 of an online mathematics course on group theory. It classifies groups of order 4 and gives several examples of products of groups.
From playlist Group theory
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 19: Wreath products
This lecture is part of an online mathematics course on group theory. It describes wreath products and gives a few examples of them, such as Sylow subgroups of symmetric 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
Visual Group Theory, Lecture 4.4: Finitely generated abelian groups
Visual Group Theory, Lecture 4.4: Finitely generated abelian groups We begin this lecture by proving that the cyclic group of order n*m is isomorphic to the direct product of cyclic groups of order n and m if and only if gcd(n,m)=1. Then, we classify all finite abelian groups by decomposi
From playlist Visual Group Theory
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
Group theory 15:Groups of order 12
This lecture is part of an online mathematics course on group theory. It uses the Sylow theorems to classify the groups of order 12, and finds their subgroups.
From playlist Group theory
Group theory 17: Finite abelian groups
This lecture is part of a mathematics course on group theory. It shows that every finitely generated abelian group is a sum of cyclic groups. Correction: At 9:22 the generators should be g, h+ng not g, g+nh
From playlist Group theory
This is lecture 9 of an online mathematics course on groups theory. It covers the quaternions group and its realtion to the ring of quaternions.
From playlist 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
Rings 10 Tensor products of abelian groups
This lecture is part of an online course on rings and modules. We define tensor products of abelian groups, and calculate them for many common examples using the fact that tensor products preserve colimits. For the other lectures in the course see https://www.youtube.com/playlist?list=P
From playlist Rings and modules
Group theory 20: Frobenius groups
This lecture is part of an online mathematics course on group theory. It gives several examples of Frobenius groups (permutation groups where any element fixing two points is the identity).
From playlist Group theory