Difference between revisions of "Isomorphism"
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Given two [[Group (mathematics)|group]]s <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 [[Bijection|bijective]].<br /><br /> | Given two [[Group (mathematics)|group]]s <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 [[Bijection|bijective]].<br /><br /> | ||
| − | Two groups <math>G,G'</math> are called '''isomorphic''' if an isomorphism from <math>G</math> to <math>G'</math> exists. | + | Two groups <math>G,G'</math> are called '''isomorphic''' if an isomorphism from <math>G</math> to <math>G'</math> exists. |
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Revision as of 02:52, August 10, 2012
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.