Results 1 to 2 of 2

Math Help - Isomorphic?

  1. #1
    Super Member
    Joined
    Mar 2006
    Posts
    705
    Thanks
    2

    Isomorphic?

    How do I show whether the pair of groups S_{5},D_{60} is isomorphic?

    I know that the order of the two groups is 120, they are both non-commutative, they are both non-cyclic. But I believe they are not isomorphic since I can't really find a function that does the trick.

    Please help, thanks!

    K
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    The only element \sigma \in S_n with n\geq 3 that has a property that \sigma \tau = \tau \sigma i.e. it commutes with everything, is \sigma = i, i.e. the identity element.*

    Now is that true for D_n, i.e. it has a trivial center? I think not. So they are non-isomorphic.





    *)If you every learned the meaning of "center" we will say the center of S_n is trivial for n\geq 3.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Isomorphic
    Posted in the Advanced Algebra Forum
    Replies: 10
    Last Post: November 8th 2010, 07:19 PM
  2. is U14 isomorphic to U18?
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: August 21st 2010, 09:52 AM
  3. Isomorphic
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: March 8th 2010, 11:13 AM
  4. Isomorphic
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: October 13th 2008, 08:55 PM
  5. Isomorphic or not?
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 13th 2008, 04:41 PM

Search Tags


/mathhelpforum @mathhelpforum