Group automorphisms in abstract algebra
Group automorphisms are bijective mappings of a group onto itself. In this tutorial I define group automorphisms and introduce the fact that a set of such automorphisms can exist. This set is proven to be a subgroup of the symmetric group. You can learn more about Mathematica on my Udem
From playlist Abstract algebra
In this video we construct a symmetric group from the set that contains the six permutations of a 3 element group under composition of mappings as our binary operation. The specifics topics in this video include: permutations, sets, groups, injective, surjective, bijective mappings, onto
From playlist Abstract algebra
Abstract Algebra: We compute the automorphism group of A4, the alternating group on 4 letters. We have that Aut(G) = S4, the symmetric group on 4 letters, Inn(A4) = A4, and Out(A4)=Z/2. We note that the coset structure splits S4 into even and odd permutations. U.Reddit course material
From playlist Abstract Algebra
Visual Group Theory, Lecture 2.3: Symmetric and alternating groups
Visual Group Theory, Lecture 2.3: Symmetric and alternating groups In this lecture, we introduce the last two of our "5 families" of groups: (4) symmetric groups and (5) alternating groups. The symmetric group S_n is the group of all n! permutations of {1,...,n}. We see several different
From playlist Visual Group Theory
GT17. Symmetric and Alternating Groups
EDIT: at 15:00, we have (abcde) = (abc)(cde) instead of (abc)(ade) Abstract Algebra: We review symmetric and alternating groups. We show that S_n is generated by its 2-cycles and that A_n is generated by its 3-cycles. Applying the latter with the Conjugation Formula, we show that A_5 i
From playlist Abstract Algebra
Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
From playlist Abstract algebra
Global symmetry from local information: The Graph Isomorphism Problem – László Babai – ICM2018
Combinatorics | Mathematical Aspects of Computer Science Invited Lecture 13.4 | 14.5 Global symmetry from local information: The Graph Isomorphism Problem László Babai Abstract: Graph Isomorphism (GI) is one of a small number of natural algorithmic problems with unsettled complexity stat
From playlist Combinatorics
Group theory 30: Outer automorphisms
This lecture is part of an online course on group theory. We find the automorphism groups of symmetric groups, and in particular show that the symmetric group on 6 points has "extra" (outer) automorphisms.
From playlist Group theory
Isomorphisms in abstract algebra
In this video I take a look at an example of a homomorphism that is both onto and one-to-one, i.e both surjective and injection, which makes it a bijection. Such a homomorphism is termed an isomorphism. Through the example, I review the construction of Cayley's tables for integers mod 4
From playlist Abstract algebra
Eisenstein series, p-adic deformations, Galois representations, and the group G_2 - Sam Mundy
Joint IAS/Princeton University Number Theory Seminar Topic: Eisenstein series, p-adic deformations, Galois representations, and the group G_2 Speaker: Sam Mundy Affiliation: Columbia University Date: April 01, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Math talk: Sporadic groups and number theory
This talk was the introduction to the Berkeley graduate number theory discussion seminar on 2020-10-28, and the aim was to explain why number theorists might be interested in sporadic simple groups. We give a brief summary of monstrous moonshine relating sporadic groups to modular functi
From playlist Math talks
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
Paul GUNNELLS - Cohomology of arithmetic groups and number theory: geometric, ... 1
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Özlem Ejder, Dynamical Belyi maps
VaNTAGe seminar, September 14, 2021 License: CC-BY-NC-SA
From playlist Belyi maps and Hurwitz spaces
Algebraic geometry 46: Examples of Hurwitz curves
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives examples of complex curves of genus 2 and 3 with the largest possible symmetry groups .
From playlist Algebraic geometry I: Varieties
Visual Group Theory, Lecture 6.2: Field automorphisms
Visual Group Theory, Lecture 6.2: Field automorphisms A field automorphism is a structure preserving map from a field F to itself. This means that it must be both a homomorphism of both the addtive group (F,+) and the multiplicative group (F-{0},*). We show that any automorphism of an ext
From playlist Visual Group Theory
Abstract Algebra - 6.5 Automorphisms
We finish up chapter 6 by discussion automorphisms and inner automorphisms. An automorphism is just a special isomorphism that maps a group to itself. An inner-automorphism uses conjugation of an element and its inverse to create a mapping. Video Chapters: Intro 0:00 What is an Automorphi
From playlist Abstract Algebra - Entire Course
Visual Group Theory, Lecture 4.6: Automorphisms
Visual Group Theory, Lecture 4.6: Automorphisms An automorphism is an isomorphism from a group to itself. The set of all automorphisms of G forms a group under composition, denoted Aut(G). After a few simple examples, we learn how Aut(Z_n) is isomorphic to U(n), which is the group consist
From playlist Visual Group Theory
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