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Isomorphic groups?

  1. Sep 24, 2008 #1

    tgt

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    If two groups A and B are isomorphic then by studying one of them, we can deduce all algebraic information about the other? Hence studying one is equivalent to studying the other?
     
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  3. Sep 24, 2008 #2

    quasar987

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    Provided you define "algebraic properties" correctly, then yes.
     
  4. Sep 24, 2008 #3

    tgt

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    Isn't algebraic properties 'clear cut'? What are some things that might be considered algebraic properties but are different in two isomorphic groups?

    Would some even define algebraic properties to be those that occur in all isomorphic groups?
     
  5. Sep 25, 2008 #4

    morphism

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    Yes: usually an algebraic property is defined as a property which is preserved under isomorphism.
     
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