Permutation Groups and Symmetric Groups | Abstract Algebra

Опубликовано: 28 Ноябрь 2022
на канале: Wrath of Math

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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 Cayley table for the symmetric group S3, and look at some inverse permutations. We also cover the definition of a permutation, which is a bijection from a set to itself.

Cayley's Theorem:    • Proof of Cayley's Theorem | Abstract ...

A proof that compositions of bijections are bijective in two parts:
   • Proof: Composition of Injective Funct...
   • Proof: Composition of Surjective Func...

Abstract Algebra Course:    • Abstract Algebra
Abstract Algebra Exercises:    • Abstract Algebra Exercises

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