Proof of Cayley's Theorem | Abstract Algebra

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Abstract Algebra course:    • Abstract Algebra  
Abstract Algebra exercises:    • Abstract Algebra Exercises  

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We go over how to prove Cayley's Theorem, which states the incredible fact that every group is isomorphic to some permutation group. This proof will require us to construct a group of permutations of G, then show that G is isomorphic to this permutation. There are a fair bit of details to work out, but it is a surprisingly straightforward proof. #abstractalgebra

Permutation Groups:    • Permutation Groups and Symmetric Groups | ...  
Isomorphic Groups:    • Isomorphic Groups and Isomorphisms in Grou...  

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0:00 Intro
0:48 Constructing Permutations
3:17 Making the Permutation Group
6:23 The Isomorphism
9:02 Conclusion