Algebraic structures

N-ary group

In mathematics, and in particular universal algebra, the concept of an n-ary group (also called n-group or multiary group) is a generalization of the concept of a group to a set G with an n-ary operation instead of a binary operation. By an n-ary operation is meant any map f: Gn → G from the n-th Cartesian power of G to G. The axioms for an n-ary group are defined in such a way that they reduce to those of a group in the case n = 2. The earliest work on these structures was done in 1904 by Kasner and in 1928 by Dörnte; the first systematic account of (what were then called) polyadic groups was given in 1940 by Emil Leon Post in a famous 143-page paper in the Transactions of the American Mathematical Society. (Wikipedia).

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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

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Abstract Algebra | The dihedral group

We present the group of symmetries of a regular n-gon, that is the dihedral group D_n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

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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

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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

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Group Theory: The Center of a Group G is a Subgroup of G Proof

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Group Theory: The Center of a Group G is a Subgroup of G Proof

From playlist Abstract Algebra

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Alain Connes - Fonctions sphéroïdales et triplets spectraux

J'explique la construction à partir de l'opérateur différentiel W du second ordre qui apparait par séparation des variables dans le Laplacien d'un ellipsoide, et des fonctions propres de W, de triplets spectraux reproduisant les comportement infrarouge et ultraviolets des zeros de zeta. Ce

From playlist Annual meeting “Arbre de Noël du GDR Géométrie non-commutative”

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Alexander Olshanskii - Relative growth of subgroups in finitely generated groups

Alexander Olshanskii (Vanderbilt University, USA and Moscow State University, Russia) Let $H$ be a subgroup of a finitely generated group $G$. The (relative) growth function $f(n)$ of $H$ with respect to a finite set $A$ generating $G$, is given by the formula $f(n) = card \{g\in H;

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

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Symmetric spaces (Lecture – 01) by Pralay Chatterjee

Geometry, Groups and Dynamics (GGD) - 2017 DATE: 06 November 2017 to 24 November 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The program focuses on geometry, dynamical systems and group actions. Topics are chosen to cover the modern aspects of these areas in which research has b

From playlist Geometry, Groups and Dynamics (GGD) - 2017

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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

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Sub-Weyl Subconvexity and Short p-Adic Exponential Sums - Djordje Milicevic

Djordje Milicevic April 17, 2012 One of the principal questions about L-functions is the size of their critical values. In this talk, we will present a new subconvexity bound for the central value of a Dirichlet L-function of a character to a prime power modulus, which breaks a long-standi

From playlist Mathematics

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The General Linear Group, The Special Linear Group, The Group C^n with Componentwise Multiplication

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys The General Linear Group, The Special Linear Group, The Group C^n with Componentwise Multiplication

From playlist Abstract Algebra

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Abstract Algebra | Group of Units modulo n

We sketch a proof that the equivalence classes of integers which are relatively prime to n form a group. This group is called the group of units modulo n. http://www.michael-penn.net

From playlist Abstract Algebra

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Paul Meunier - Quantum Automorphism Groups of Some Classes of Graphs

Simple combinatorial objects like finite graphs can reveal hidden endemically quantum behaviors. In the same way that the symmetries of a graph are encoded in its automorphism group, its quantum symmetries are encoded in its quantum automorphism group. Surprisingly, the latter can be very

From playlist Annual meeting “Arbre de Noël du GDR Géométrie non-commutative”

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Lec 19 | MIT 6.450 Principles of Digital Communications I, Fall 2006

Lecture 19: Baseband detection and complex Gaussian processes View the complete course at: http://ocw.mit.edu/6-450F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.450 Principles of Digital Communications, I Fall 2006

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Big Think Interview With Dan Ariely | Big Think

Big Think Interview With Dan Ariely New videos DAILY: https://bigth.ink/youtube Join Big Think Edge for exclusive videos: https://bigth.ink/Edge ---------------------------------------------------------------------------------- A conversation with the author of "Predictably Irrational" an

From playlist Dan Ariely | Big Think

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Bertrand Eynard: (Mixed) topological recursion and the two-matrix model - Lecture 1

Mini course of the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: In this series of lecture we will introduce the 2-matrix model and the issue of mixed traces, then we shall give the answers as formulas. Some formulas will be

From playlist Noncommutative geometry meets topological recursion 2021

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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

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How To Create LoL Character Figurine Creation In Zbrush 4R8 | Session 01 | #gamedev

Don’t forget to subscribe! In this project series, you will learn to create LoL character figurine in Zbrush. In this tutorial, you'll be learning how to create a League of Legends character with movable limbs in Zbrush 4R8. The character will be 3d Printable. Introduction: https:/

From playlist Create LoL Character Figurine Creation In Zbrush 4R8

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(7.2.1B) Power Series Solutions to Second Order Linear ODEs: y''-xy=1 (Airy's Equation)

This video explains how to determine a power series solution to a second order linear ordinary differential equation. https://mathispower4u.com

From playlist Differential Equations: Complete Set of Course Videos

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The Special Linear Group is a Subgroup of the General Linear Group Proof

The Special Linear Group is a Subgroup of the General Linear Group Proof

From playlist Abstract Algebra

Related pages

Emil Leon Post | Axiom | Mathematics | Magma (algebra) | Universal algebra | Arity | Group (mathematics)