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 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
Get the textbook for this course! https://amzn.to/3IjoZaO
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