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#### pauloromero1983

##### New member

- Jul 21, 2020

- 2

My question is how to arrive to such conclusion. Im aware that, for every ordered pair of \(G\times G\) theres \(n\) images (since \(X\) was assumed to have \(n\) elements). For a concrete example, let be \(G\) a group of 2 elements. Then, there are 4 ordered pairs. Each pair has 2 images, so the total number of maps would be 4*2=8. However, by use of the relation \(n^{n^{2}}\) we get \(2^{2^{2}}=16\), i.e, there are 16 different maps, not 8. Im missing something here, but I dont know what exactly what the error is.