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
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
Automorphism groups and modular arithmetic
Jacob explains the concept of the automorphism group of a group, as well as how such groups give rise to useful properties of multiplication in modular arithmetic, including Fermat's Little Theorem.
From playlist Basics: Group Theory
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
In this tutorial I present the cyclic group of three elements as a group automorphism. You can learn more about Mathematica on my Udemy courses: https://www.udemy.com/mathematica/ https://www.udemy.com/mathematica-for-statistics/
From playlist Abstract algebra
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
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
EDIT: At 3:20, nonzero elements have order 3, not 2. Abstract Algebra: We consider the group Aut(G) of automorphisms of G, the isomorphisms from G to itself. We show that the inner automorphisms of G, induced by conjugation, form a normal subgroup Inn(G) of Aut(G), and that Inn(G) is i
From playlist Abstract Algebra
Example of Group Automorphism 1 (Requires Linear Algebra)
Matrix Theory: We compute the automorphism groups of G = Z/10 and G=Z/2 x Z/2. The first case is a warm up for Part 2. The second case can be recast as a linear algebra problem with matrix groups.
From playlist Matrix Theory
Jason Parker - Covariant Isotropy of Grothendieck Toposes
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/ParkerSlidesToposesOnline.pdf Covariant isotropy can be regarded as providing an abstract notion of conjugation or i
From playlist Toposes online
Zlil Sela - Automorphisms of groups and a higher rank JSJ decomposition
The JSJ (for groups) was originally constructed to study the automorphisms and the cyclic splittings of a (torsion-free) hyperbolic group. Such a structure theory was needed to complete the solution of the isomorphism problem for (torsion-free) hyperbolic groups. Later, the JSJ was genera
From playlist Geometry in non-positive curvature and Kähler groups
Alexander HULPKE - Computational group theory, cohomology of groups and topological methods 5
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
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
Non-amenable groups admitting no sofic approximation by expander graphs - Gabor Kun
Stability and Testability Topic: Non-amenable groups admitting no sofic approximation by expander graphs Speaker: Gabor Kun Affiliation: Alfréd Rényi Institute of Mathematics Date: February 10, 2021 For more video please visit http://video.ias.edu
From playlist Stability and Testability
Karen Vogtmann: The geometry and topology of automorphism groups of free groups
HYBRID EVENT Recorded during the meeting "Groups Acting on Fractals" the April 11, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Ma
From playlist Topology
Differential Isomorphism and Equivalence of Algebraic Varieties Board at 49:35 Sum_i=1^N 2/(x-phi_i(y,t))^2
From playlist Fall 2017
Group Isomorphisms in Abstract Algebra
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Group Isomorphisms in Abstract Algebra - Definition of a group isomorphism and isomorphic groups - Example of proving a function is an Isomorphism, showing the group of real numbers under addition is isomorphic to the group of posit
From playlist Abstract Algebra
CTNT 2022 - An Introduction to Galois Representations (Lecture 1) - 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/
From playlist CTNT 2022 - An Introduction to Galois Representations (by Alvaro Lozano-Robledo)