Finitely generated group

Cyclic groups and finite groups

Jacob goes into detail on some particularly important finite groups, and explains how groups and subgroups can be generated by their elements, along with some important consequences.

From playlist Basics: 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

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

Every Group is a Quotient of a Free Group

First isomorphism theorem: https://youtu.be/ssVIJO5uNeg An explanation of a proof that every finite group is a quotient of a free group. A similar proof also applies to infinite groups because we can consider a free group on an infinite number of elements! Group Theory playlist: https://

From playlist Group Theory

GT2. Definition of Subgroup

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 31: Free groups

This lecture is part of an online math course on group theory. We review free abelian groups, then construct free (non-abelian) groups, and show that they are given by the set of reduced words, and as a bonus find that they are residually finite.

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

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

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

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

Profinite rigidity – Alan Reid – ICM2018

Topology Invited Lecture 6.7 Profinite rigidity Alan Reid Abstract: We survey recent work on profinite rigidity of residually finite groups. © International Congress of Mathematicians – ICM www.icm2018.org     Os direitos sobre todo o material deste canal pertencem ao Instituto de Mat

From playlist Topology

Genevieve Walsh: Incoherence of free-by-free and surface-by-freegroups

CIRM VIRTUAL EVENT Recorded during the meeting"Virtual Geometric Group Theory conference " the May 29, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM

From playlist Virtual Conference

Bettina EICK - Computational group theory, cohomology of groups and topological methods 1

The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computation

From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory

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

Laurent Bartholdi - Imbeddings in groups of subexponential growth

Laurent Bartholdi (University of Gottingen, Germany) A finitely generated group has subexponential growth if the number of group elements expressible as words of length $\le n$ grows subexponentially in $n$. I will show that every countable group that does not contain a subgroup of expone

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

Stability and Invariant Random Subgroups - Henry Bradford

Stability and Testability Topic: Stability and Invariant Random Subgroups Speaker: Henry Bradford Affiliation: Cambridge University Date: January 20, 2021 For more video please visit http://video.ias.edu

From playlist Stability and Testability

Model Theory of Fields with Virtually Free Group Action - Ö. Beyarslan - Workshop 3 - CEB T1 2018

Özlem Beyarslan (Boğaziçi University) / 29.03.2018 Model Theory of Fields with Virtually Free Group Action This is joint work with Piotr Kowalski. A G-field is a field, together with an acion of a group G by field automorphisms. If an axiomatization for the class of existentially closed

From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields

Ultrametric stability problems - Francesco Fournier Facio

Stability and Testability Topic: Ultrametric stability problems Speaker: Francesco Fournier Facio Affiliation: Eidgenössische Technische Hochschule Zürich Date: March 31, 2021 For more video please visit http://video.ias.edu

From playlist Stability and Testability

algebraic geometry 12 Hilbert's finiteness theorem

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the proof of Hilbert's finiteness theorem for rings of invariants. (This is not the same as Hilbert's finiteness theorem for ideals, though the two theorems are

From playlist Algebraic geometry I: Varieties

Definition of a Cyclic Group with Examples

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Cyclic Group with Examples

From playlist Abstract Algebra