In mathematics, the Thompson groups (also called Thompson's groups, vagabond groups or chameleon groups) are three groups, commonly denoted , that were introduced by Richard Thompson in some unpublished handwritten notes in 1965 as a possible counterexample to the von Neumann conjecture. Of the three, F is the most widely studied, and is sometimes referred to as the Thompson group or Thompson's group. The Thompson groups, and F in particular, have a collection of unusual properties that have made them counterexamples to many general conjectures in group theory. All three Thompson groups are infinite but finitely presented. The groups T and V are (rare) examples of infinite but finitely-presented simple groups. The group F is not simple but its derived subgroup [F,F] is and the quotient of F by its derived subgroup is the free abelian group of rank 2. F is totally ordered, has exponential growth, and does not contain a subgroup isomorphic to the free group of rank 2. It is conjectured that F is not amenable and hence a further counterexample to the long-standing but recently disprovedvon Neumann conjecture for finitely-presented groups: it is known that F is not elementary amenable. introduced an infinite family of finitely presented simple groups, including Thompson's group V as a special case. (Wikipedia).
Mark Sapir: On subgroups of the R. Thompson group F
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
From playlist Music.
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
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
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
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
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
Music - "Reunited" by RH Soundtracks http://www.rhsoundtracks.net/
From playlist BAGUETTE
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
The Abel Prize announcement 2008 - John Thompson and Jacques Tits
0:00 Welcome by chair of the Mathematics group in The Norwegian Academy of Science and Letters, Tom Lyche 1:45 The Abel Prize announced by Ole Didrik Lærum, President of The Norwegian Academy of Science and Letters 2:41 Citation by Kristian Seip, Chair of the Abel committee 8:18 Professor
From playlist John Griggs Thompson
Algorithms for groups of homeomorphisms - Susan Hermiller
Women and Mathematics Title: Algorithms for groups of homeomorphisms Speaker: Susan Hermiller Affiliation: University of Nebraska Date: May 23, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Michel Broué: Building Cathedrals and breaking down Reinforced Concrete Walls
This lecture was held at The University of Oslo, May 21, 2008 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations. Program for the Abel Lectures 2008 1. Abel Laureate John Thompson: “Dirichlet series and SL(2,Z)" 2. Abel Laureate Jacques Tits: “Alg
From playlist Abel Lectures
Marcus du Sautoy: Symmetry explained
Marcus Peter Francis du Sautoy is a British mathematician, author, and populariser of science and mathematics. You can view more content of Marcus du Sautoy here: https://www.youtube.com/channel/UCYF21Xc9fSdqVWRxpBAOleQ/featured This video is a clip from the Abel Prize Announcement 2008.
From playlist Popular presentations
Geometry of Growth and Form: Commentary on D'Arcy Thompson | John Milnor
John Milnor, Co-Director of the Institute for Mathematical Sciences at Stony Brook University http://www.math.sunysb.edu/~jack September 24, 2010 In this lecture, John Milnor, Co-Director of the Institute for Mathematical Sciences at Stony Brook University and a former member of the Facul
From playlist Mathematics
Marjorie Wikler Senechal - Unwrapping a Gem - CoM Apr 2021
If the celebrated Scottish zoologist D’Arcy W. Thompson (1860 – 1948) could have met the near-legendary German astronomer Johannes Kepler (1571 – 1630), what would they talk about? Snowflakes, maybe? It is true that both men wrote about their hexagonal shapes. But they both wrote about Arc
From playlist Celebration of Mind 2021
Kristen Ghodsee - October 14, 2016
AMIAS Public Lectures "The Left Side of History: World War II and Re-emergent Nationalisms in Contemporary Eastern Europe" Kristen Ghodsee, Professor and Director of Gender, Sexuality, and Women’s Studies at Bowdoin College, former Member (2006–07) in the School of Social Science, and Pre
From playlist AMIAS
Justin Lynd: Control of fixed points and centric linking systems
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: Workshop "Fusion systems and equivariant algebraic topology"
From playlist HIM Lectures: Junior Trimester Program "Topology"
General discussion - Steven Lukes
Au coeur de l'Etat Comment les institutions traitent leur public International Conference supported by the European Research Council École des Hautes Études en Sciences Sociales (Paris) and Institute for Advanced Study (Princeton) Paris, 11 & 12 June 2012 More videos on http://video.ias
From playlist Social Science
8ECM Invited Lecture: Aner Shalev
From playlist 8ECM Invited Lectures
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