proof of Cayley’s theorem
Define by . Then is a homomorphism, since
And is injective, since if then , so for all , and so as required.
So is an embedding of into its own permutation group. If is finite of order , then simply numbering the elements of gives an embedding from to .
|Title||proof of Cayley’s theorem|
|Date of creation||2013-03-22 12:30:50|
|Last modified on||2013-03-22 12:30:50|
|Last modified by||Evandar (27)|