Permutation group

Permutation Groups and Symmetric Groups | Abstract Algebra

We introduce permutation groups and symmetric groups. We cover some permutation notation, composition of permutations, composition of functions in general, and prove that the permutations of a set make a group (with certain details omitted). #abstractalgebra #grouptheory We will see the

From playlist Abstract Algebra

301.5A Permutation Groups: Intro and Goals

Goals for studying the properties of permutation groups. Plus, anagrams!

From playlist Modern Algebra - Chapter 16 (permutations)

Symmetric groups

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

Chapter 16 - Permutations

This project was created with Explain Everything™ Interactive Whiteboard for iPad.

From playlist Modern Algebra - Chapter 16 (permutations)

GT17.1. Permutation Matrices

Abstract Algebra: (Linear Algebra Required) The symmetric group S_n is realized as a matrix group using permutation matrices. That is, S_n is shown to the isomorphic to a subgroup of O(n), the group of nxn real orthogonal matrices. Applying Cayley's Theorem, we show that every finite gr

From playlist Abstract Algebra

301.5C Definition and "Stack Notation" for Permutations

What are permutations? They're *bijective functions* from a finite set to itself. They form a group under function composition, and we use "stack notation" to denote them in this video.

From playlist Modern Algebra - Chapter 16 (permutations)

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

7.2.3 Permutation Matrices Part 3

7.2.3 Permutation Matrices Part 3

From playlist Week 7

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

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

L23.3 Permutation operators on N particles and transpositions

MIT 8.06 Quantum Physics III, Spring 2018 Instructor: Barton Zwiebach View the complete course: https://ocw.mit.edu/8-06S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60Zcz8LnCDFI8RPqRhJbb4L L23.3 Permutation operators on N particles and transpositions License: Cr

From playlist MIT 8.06 Quantum Physics III, Spring 2018

Visual Group Theory, Lecture 2.4: Cayley's theorem

Visual Group Theory, Lecture 2.4: Cayley's theorem Cayley's theorem says that every finite group has the same structure as some collection of permutations. Formally, this means that every finite group is isomorphic to a subgroup of some symmetric group. In this lecture, we see two ways to

From playlist Visual Group Theory

Cayley's Theorem Explanation: Every Group is a Permutation Group

Functions with two-sided inverse are bijective: https://youtu.be/XnkgXYvwJZw First isomorphism theorem explanation: https://youtu.be/ssVIJO5uNeg Proof that every group is isomorphic to a subgroup of the symmetric group. We use group actions to derive this very interesting fact in group

From playlist Group Theory

Group theory 22: Symmetric groups

This lecture is part of an online mathematics course on group theory. It covers the basic theory of symmetric and alternating groups, in particular their conjugacy classes.

From playlist Group theory

301.5B Motivating Permutations: Anagrams and Symmetries

Permutations are of interest for several reasons in mathematics. Here we argue for why the dihedral group of the triangle is "the same" as the group of permutations of three symbols (the vertices of that triangle).

From playlist Modern Algebra - Chapter 16 (permutations)

Visual Group Theory, Lecture 5.1: Groups acting on sets

Visual Group Theory, Lecture 5.1: Groups acting on sets When we first learned about groups as collections of actions, there was a subtle but important difference between actions and configurations. This is the tip of the iceberg of a more general and powerful concept of a group action. Ma

From playlist Visual Group Theory