In mathematics, in the field of group theory, a group is said to be absolutely simple if it has no proper nontrivial serial subgroups. That is, is an absolutely simple group if the only serial subgroups of are (the trivial subgroup), and itself (the whole group). In the finite case, a group is absolutely simple if and only if it is simple. However, in the infinite case, absolutely simple is a stronger property than simple. The property of being strictly simple is somewhere in between. (Wikipedia).

Simple Groups - Abstract Algebra

Simple groups are the building blocks of finite groups. After decades of hard work, mathematicians have finally classified all finite simple groups. Today we talk about why simple groups are so important, and then cover the four main classes of simple groups: cyclic groups of prime order

From playlist Abstract Algebra

Chapter 5: Quotient groups | Essence of Group Theory

Quotient groups is a very important concept in group theory, because it has paramount importance in group homomorphisms (connection with the isomorphism theorem(s)). With this video series, abstract algebra needs not be abstract - one can easily develop intuitions for group theory! In fac

From playlist Essence of Group Theory

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

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

Simple groups, Lie groups, and the search for symmetry II | Math History | NJ Wildberger

This is the second video in this lecture on simple groups, Lie groups and manifestations of symmetry. During the 19th century, the role of groups shifted from its origin in number theory and the theory of equations to its role in describing symmetry in geometry. In this video we talk abou

From playlist MathHistory: A course in the History of Mathematics

A group is (in a sense) the simplest structure in which we can do the familiar tasks associated with "algebra." First, in this video, we review the definition of a group.

From playlist Modern Algebra - Chapter 15 (groups)

Simple groups, Lie groups, and the search for symmetry I | Math History | NJ Wildberger

During the 19th century, group theory shifted from its origins in number theory and the theory of equations to describing symmetry in geometry. In this video we talk about the history of the search for simple groups, the role of symmetry in tesselations, both Euclidean, spherical and hyper

From playlist MathHistory: A course in the History of Mathematics

Imprimitive irreducible representations of finite quasisimple groups by Gerhard Hiss

DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra

From playlist Group Theory and Computational Methods

Daniel Hoffmann, University of Warsaw

May 14, Daniel Hoffmann, University of Warsaw Fields with derivations and action of finite group

From playlist Spring 2021 Online Kolchin Seminar in Differential Algebra

Jochen Koenigsmann : Galois codes for arithmetic and geometry via the power of valuation theory

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

Nero Budur: Absolute sets and the Decomposition Theorem

Abstract: We give a new, more conceptual proof of the Decomposition Theorem for semisimple perverse sheaves of rank-one origin, assuming it for those of constant-sheaf origin, that is, assuming the geometric case proven by Beilinson-Bernstein-Deligne-Gabber. Joint work with Botong Wang. R

From playlist Algebraic and Complex Geometry

Operator Scaling via Geodesically Convex Optimization, Invariant Theory... - Yuanzhi Li

Optimization, Complexity and Invariant Theory Topic: Operator Scaling via Geodesically Convex Optimization, Invariant Theory and Polynomial Identity Testing Speaker: Yuanzhi Li Affiliation: Princeton University Date: June 7. 2018 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Endomorphisms of certain superelliptic jacobians and l-adic (..) - Zarhin - Workshop 2 - CEB T2 2019

Yuri Zarhin (Pennsylvania State University) / 28.06.2019 Endomorphisms of certain superelliptic jacobians and l-adic Lie algebras The subject of this talk is a certain explicitly constructed class of superelliptic jacobians defined over global fields with small endomorphism rings. We al

From playlist 2019 - T2 - Reinventing rational points

Spectra in locally symmetric spaces by Alan Reid

PROGRAM ZARISKI-DENSE SUBGROUPS AND NUMBER-THEORETIC TECHNIQUES IN LIE GROUPS AND GEOMETRY (ONLINE) ORGANIZERS: Gopal Prasad, Andrei Rapinchuk, B. Sury and Aleksy Tralle DATE: 30 July 2020 VENUE: Online Unfortunately, the program was cancelled due to the COVID-19 situation but it will

From playlist Zariski-dense Subgroups and Number-theoretic Techniques in Lie Groups and Geometry (Online)

Support Varieties for Modular Representations - Eric M. Friedlander

Members’ Seminar Topic: Support Varieties for Modular Representations Speaker: Eric M. Friedlander Affiliation: University of Southern California; Member, School of Mathematics Date: November 30, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

CTNT 2022 - An Introduction to Galois Representations (Lecture 4) - by Alvaro Lozano-Robledo

This video is part of a mini-course on "An Introduction to Galois Representations" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/ Note: I was tired after a long event, and may have missp

From playlist CTNT 2022 - An Introduction to Galois Representations (by Alvaro Lozano-Robledo)

Group Definition (expanded) - Abstract Algebra

The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin

From playlist Abstract Algebra

Graphs, vectors and integers - Noga Alon

Noga Alon Tel Aviv University; Visiting Professor, School of Mathematics December 1, 2014 The study of Cayley graphs of finite groups is related to the investigation of pseudo-random graphs and to problems in Combinatorial Number Theory, Geometry and Information Theory. I will discuss thi

From playlist Mathematics