1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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)>.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Showing Subgroups of a Permutation Group are Isomorphic
Loading...