Dihedral group

Abstract Algebra | The dihedral group

We present the group of symmetries of a regular n-gon, that is the dihedral group D_n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

Dihedral group example

In this veideo we continue our look in to the dihedral groups, specifically, the dihedral group with six elements. We note that two of the permutation in the group are special in that they commute with all the other elements in the group. In the next video I'll show you that these two el

From playlist Abstract algebra

Dihedral Group (Abstract Algebra)

The Dihedral Group is a classic finite group from abstract algebra. It is a non abelian groups (non commutative), and it is the group of symmetries of a regular polygon. This group is easy to work with computationally, and provides a great example of one connection between groups and geo

From playlist Abstract Algebra

Group theory 13: Dihedral groups

This lecture is part of an online mathematics course on group theory. It covers some basic properties of dihedral groups.

From playlist Group theory

Visual Group Theory, Lecture 2.2: Dihedral groups

Cyclic groups describe the symmetry of objects that exhibit only rotational symmetry, like a pinwheel. Dihedral groups describe the symmetry of objects that exhibit rotational and reflective symmetry, like a regular n-gon. The corresponding dihedral group D_n has 2n elements: half are rota

From playlist Visual Group Theory

Dihedral groups in abstract algebra

In the previous video I showed a square and its symmetric transformations. This is actually a dihedral group in four elements. In this video I explain what a dihedral group is, but way of visual examples and the selection of permutations of a set. At the end I use the Wolfram Language t

From playlist Abstract algebra

Center of a group in abstract algebra

After the previous video where we saw that two of the elements in the dihedral group in six elements commute with all the elements in the group, we finally get to define the center of a group. The center of a group is a subgroup and in this video we also go through the proof to show this.

From playlist Abstract algebra

Group Theory II Symmetry Groups

Why are groups so popular? Well, in part it is because of their ability to characterise symmetries. This makes them a powerful tool in physics, where symmetry underlies our whole understanding of the fundamental forces. In this introduction to group theory, I explain the symmetry group of

From playlist Foundational Math

GT18.1. Class Equation for Dihedral Groups

Abstract Algebra: We consider the class equation for the dihedral groups D_2n. Conjugacy classes are computed, and we verify the cardinality equation using centralizers. To finish, we consider the partitions for normal subgroups. U.Reddit course materials available at http://ureddit.co

From playlist Abstract Algebra

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

Abstract Algebra - 1.3 The Dihedral Groups

Building on what we now know about the symmetries of a square, we generalize to what we can determine about any of the dihedral groups for n=3 or greater for regular n-gons (equilateral triangle, square, regular pentagon, etc.) Video Chapters: Intro 0:00 Recap of Cayley Tables 0:08 D3, D4

From playlist Abstract Algebra - Entire Course

Sophie Morel - Intersection cohomology of Shimura varieties and pizza

Correction: The affiliation of Lei Fu is Tsinghua University. Given a disc in the plane select any point in the disc and cut the disc by four lines through this point that are equally spaced. We obtain eight slices of the disc, each having angle π/4 at the point. The pizza theorem says th

From playlist Conférence « Géométrie arithmétique en l’honneur de Luc Illusie » - 5 mai 2021

GT5. Index 2 Theorem and Dihedral Groups

EDIT: typo at 12:00, it should be "0 less than/equals k less than n", so as to include e and C. Abstract Algebra: We state and prove the Index Two Theorem for finding normal subgroup and list several examples. These include S3, A4, and the symmetry groups for the regular n-gon, D_2n.

From playlist Abstract Algebra

Why Normal Subgroups are Necessary for Quotient Groups

Proof that cosets are disjoint: https://youtu.be/uxhAUmgSHnI In order for a subgroup to create a quotient group (also known as factor group), it must be a normal subgroup. That means that when we conjugate an element in the subgroup, it stays in the subgroup. In this video, we explain wh

From playlist Group Theory

The Simplifying Synthesis Ultimate Guide To Conformational Analysis

A chemistry lecture on the conformational analysis of organic compounds. Timestamps: Newman projections, nomenclature 0:42 Alkane Conformation 1:42 Allylic Strain 7:10 Cyclic Systems 11:14 Cyclohexane Substituent Effects: Heterocycles, Anomeric Effect 13.39 Fused Ring Systems: Conformati

From playlist Ultimate Guides