Isomorphism
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Given two groups <math>G,G'</math>, an isomorphism from <math>G</math> to <math>G'</math> is a function <math>\phi : G \to G'\,</math> such that <math>\phi</math> is a homomorphism and <math>\phi</math> is bijective.
Two groups <math>G,G'</math> are called isomorphic if an isomorphism from <math>G</math> to <math>G'</math> exists.