Properties of groups | Solvable groups

Metacyclic group

In group theory, a metacyclic group is an extension of a cyclic group by a cyclic group. That is, it is a group G for which there is a short exact sequence where H and K are cyclic. Equivalently, a metacyclic group is a group G having a cyclic normal subgroup N, such that the quotient G/N is also cyclic. (Wikipedia).

Video thumbnail

Math Professors Be Like...

Subscribe to mah boi @EpicMathTime! More Skits: https://www.youtube.com/watch?v=J4gcgPz26_I&list=PLN2B6ZNu6xmeTyhyB46BtiX84ANMU5n0U&index=1 Here you can find all the merch worn in the video :) https://teespring.com/stores/papaflammy My Personal favorites: https://youtu.be/Dr4egte_pwI http

From playlist Skits

Video thumbnail

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

Video thumbnail

On the pioneering works of Professor I.B.S. Passi by Sugandha Maheshwari

PROGRAM GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fund

From playlist Group Algebras, Representations And Computation

Video thumbnail

What are Functional Groups? | Biology | Biochemistry

In biological molecules, the carbon skeleton determines their general 3D shape. But what’s on the surface of the molecules determines their chemical behavior. Small chemical species, hanging off the exterior of these molecules, bump into each other and react. These are known as FUNCTIONAL

From playlist Biology

Video thumbnail

Functional Groups

This organic chemistry video tutorial provides a basic introduction into functional groups. It covers alkanes, alkenes, alkynes, aromatic rings, alcohols, ethers, esters, carboxylic acids, ketones, aldehydes, acid chlorides, acid anhydrides, amines, amides, nitriles, thiols, thioethers, t

From playlist New Organic Chemistry Playlist

Video thumbnail

Diatomic Elements & Molecules

This chemistry video tutorial provides a basic introduction into diatomic elements and molecules with their corresponding lewis structures. My Website: https://www.video-tutor.net Patreon Donations: https://www.patreon.com/MathScienceTutor Amazon Store: https://www.amazon.com/shop/theo

From playlist New AP & General Chemistry Video Playlist

Video thumbnail

Nomenclature of Polycyclic Compounds: Naphthalene, Biphenyl, Anthracene, Spiro, Bicyclo

We've done tons of IUPAC nomenclature for simple molecules, but once we start introducing multiple rings, things get trickier. This is especially the case because there are so many ways to get multiple rings. They can be fused, they can be bicyclic, aromatic or aliphatic, and every type ha

From playlist Organic Chemistry

Video thumbnail

GROUP - a quick definition

A quick definition of groups on the periodic table. Chem Fairy: Louise McCartney Director: Michael Harrison Written and Produced by Kimberly Hatch Harrison ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : https://www.patreon.com/socratica ► Make a one-time PayPal donation

From playlist Chemistry glossary

Video thumbnail

Periodic Table Part 6: Pnictogens (N, P, As, Sb, Bi, Mc)

It's time to check out Group 15 on the periodic table, the pnictogens. This includes nitrogen, phosphorus, arsenic, antimony, bismuth, and moscovium. What can we say about their properties, reactivities, and applications? Let's find out! Watch the whole Inorganic/Organometallic Chemistry

From playlist Inorganic/Organometallic Chemistry

Video thumbnail

Cyclic Groups (Abstract Algebra)

Cyclic groups are the building blocks of abelian groups. There are finite and infinite cyclic groups. In this video we will define cyclic groups, give a list of all cyclic groups, talk about the name “cyclic,” and see why they are so essential in abstract algebra. Be sure to subscribe s

From playlist Abstract Algebra

Video thumbnail

Quotient groups

The idea of a quotient group follows easily from cosets and Lagrange's theorem. In this video, we start with a normal subgroup and develop the idea of a quotient group, by viewing each coset (together with the normal subgroup) as individual mathematical objects in a set. This set, under

From playlist Abstract algebra

Video thumbnail

Lie Groups and Lie Algebras: Lesson 39 - The Universal Covering Group

Lie Groups and Lie Algebras: Lesson 39 - The Universal Covering Group We are finally in position to understand the nature of the Universal Covering Group and its connection to all the Lie groups which share a single Lie algebra. This is a critical lecture! In this lecture we simply state

From playlist Lie Groups and Lie Algebras

Video thumbnail

Lie groups: Introduction

This lecture is part of an online graduate course on Lie groups. We give an introductory survey of Lie groups theory by describing some examples of Lie groups in low dimensions. Some recommended books: Lie algebras and Lie groups by Serre (anything by Serre is well worth reading) Repre

From playlist Lie groups

Video thumbnail

Why Are Prejudice and Conflict So Common? | Understanding the Mysteries of Human Behavior

It's no wonder discrimination seems to be everywhere: splitting people into two groups, even at random, makes them subconsciously dislike each other. A sense of competition can exaggerate these feelings. Pick up your tools; we've got some bridge building to do. Presented by Mark Leary Lea

From playlist Latest Uploads

Video thumbnail

Lie Groups and Lie Algebras: Lesson 38 - Preparation for the concept of a Universal Covering Group

Lie Groups and Lie Algebras: Lesson 38 - Preparation for the Universal Covering Group concept In this lesson we examine another amazing connection between the algebraic properties of the Lie groups with topological properties. We will lay the foundation to understand how discrete invaria

From playlist Lie Groups and Lie Algebras

Video thumbnail

Grothendieck Pairs and Profinite Rigidity - Martin Bridson

Arithmetic Groups Topic: Grothendieck Pairs and Profinite Rigidity Speaker: Martin Bridson Affiliation: Oxford University Date: January 26, 2022 If a monomorphism of abstract groups H↪G induces an isomorphism of profinite completions, then (G,H) is called a Grothendieck pair, recalling t

From playlist Mathematics

Video thumbnail

Regular permutation groups and Cayley graphs

Cheryl Praeger (University of Western Australia). Plenary Lecture from the 1st PRIMA Congress, 2009. Plenary Lecture 11. Abstract: Regular permutation groups are the 'smallest' transitive groups of permutations, and have been studied for more than a century. They occur, in particular, as

From playlist PRIMA2009

Video thumbnail

Vincent Guirardel: Natural subgroups of automorphisms

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Algebra

Video thumbnail

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

Video thumbnail

Gilbert Levitt - Vertex finiteness for relatively hyperbolic groups

Gilbert Levitt (University of Caen, France) Given a finitely generated group G, we consider all splittings of G over subgroups in a fixed family (such as finite groups, cyclic groups, abelian groups). We discuss whether it is the case that only finitely many vertex groups appear, up to is

From playlist T1-2014 : Random walks and asymptopic geometry of groups.

Related pages

Square-free integer | Group extension | Normal subgroup | Quotient group | Z-group | Dihedral group | Group theory | Semidirect product | Supersolvable group | Cyclic group | Finite group | Quasidihedral group | Direct product of groups | Dicyclic group