Direct product of groups

Visual Group Theory, Lecture 3.4: Direct products

Visual Group Theory, Lecture 3.4: Direct products There is a natural way to put a group structure on the Cartesian product of two groups. In this lecture, we introduce this concept algebraically, and show several different ways to visualize this, using tools such as Cayley diagrams and mu

From playlist Visual Group Theory

Product 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

Direct Products of Groups (Abstract Algebra)

The direct product is a way to combine two groups into a new, larger group. Just as you can factor integers into prime numbers, you can break apart some groups into a direct product of simpler groups. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu

From playlist Abstract Algebra

Abstract Algebra | Internal direct product of subgroups.

We give the definition of an internal direct product of subgroups, prove a result, and give some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

Direct Products of Finite Cyclic Groups Video 2

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Direct Products of Finite Cyclic Groups Video 2. How to determine if the direct product of finite cyclic groups is cyclic. Better examples than the first video.

From playlist Abstract Algebra

Product group example

There is no better way of understanding product groups than working through and example. In this video we look at the product group of the cyclic group with two elements and itself. The final result is isomorphic to what we call the Klein 4 group.

From playlist Abstract algebra

Abstract Algebra | Direct product of groups.

We determine when the direct product of cyclic groups is cyclic. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

GT21. Internal Products

Abstract Algebra: We consider conditions for when a group is isomorphic to a direct or semidirect product. Examples include groups of order 45, 21, and cyclic groups Z/mn, where m,n are relatively prime. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-grou

From playlist Abstract Algebra

Direct Products of Finite Cyclic Groups Video 1

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Direct Products of Finite Cyclic Groups Video 1. How to determine if a direct product of finite cyclic groups is itself cyclic. This video has very easy examples.

From playlist Abstract Algebra

Martin Bridson - Subgroups of direct products of surface groups

After reviewing what is known about subgroups of direct products of surface groups and their significance in the story of which groups are Kähler, I shall describe a new construction that provides infinite families of finitely presented subgroups. These subgroups have varying higher-finite

From playlist Geometry in non-positive curvature and Kähler groups

Abstract Algebra - 8.1 External Direct Products

Let's explore how we can create new groups using existing groups. We do that by essentially creating the cartesian product of the existing groups. We look at the properties associated with these products and delve into how to show isomorphisms between an external direct product and existin

From playlist Abstract Algebra - Entire Course

GT14. Semidirect Products

EDIT: At 6:24, the product should be "(e sub H, e sub N)", not "(e sub H, e sub G)" Abstract Algebra: Using automorphisms, we define the semidirect product of two groups. We prove the group property and construct various examples, including the dihedral groups. As an application, we

From playlist Abstract Algebra

Invariant Measures for Horospherical Flows by Hee Oh

PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis

From playlist Ergodic Theory and Dynamical Systems 2022

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

Lie Groups and Lie Algebras: Lesson 41: Elementary Representation Theory I

Lie Groups and Lie Algebras: Lesson 41: Elementary Representation Theory I I wanted to begin a more intricate example of the principle of a Universal Covering group, but I think I need to cover a little background material. We need to get a grip on what is meant by "Representation Theory"

From playlist Lie Groups and Lie Algebras

Inner Semidirect Product Example: Dihedral Group

Semidirect products explanation: https://youtu.be/Pat5Qsmrdaw Semidirect products are very useful in group theory. To understand why, it's helpful to see an example. Here we show how to write the dihedral group D_2n as a semidirect product, and how we can describe that purely using cyclic

From playlist Group Theory

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