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Showing Subgroups of a Permutation Group are Isomorphic

  1. Mar 5, 2009 #1
    Define two subgroups of S6:
    G=[e, (123), (123)(456)]
    H=[e, (14), (123)(456)]

    Determine whether G and H are isomorphic.

    It seems as if they should be since they have the same cardinality and you can certainly map the elements to one another, but I don't know what other factors need to be considered when deciding whether they are isomorphic.
  2. jcsd
  3. Mar 5, 2009 #2
    H is not a subgroup since (14)(123)(456) = (123456) which is not in H. Are you sure you've written down the correct group?
  4. Mar 5, 2009 #3
    Oops. I meant G=<(123), (123)(456)> and H=<(14), (123)(456)>.
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