Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How do I find an isomorphism between Sn+m and Zn x Zm?

  1. Mar 13, 2007 #1
    How do I find an isomorphism between Sn+m and Zn x Zm? provided n,m are not relatively prime? Thanks.
     
  2. jcsd
  3. Mar 14, 2007 #2

    AKG

    User Avatar
    Science Advisor
    Homework Helper

    I dunno, place an ad in the classifieds, put up posters, etc. Or maybe start by defining what you even mean by Sn+m, because in the standard notation, Sn+m is a group that's generally not isomorphic to Zn x Zm. Also, post this in the homework section, follow the guidelines for posting homework, and when you start a new thread in the homework section, use the template that will be given to you.
     
  4. Mar 14, 2007 #3
    Hi, this isn't exactly a homework question... Anyways, rereading my question again, I made a mistake. It should be how do I find an isomorphism between A SUBGROUP in Sn+m and Zn x Zm. If it is specific cases like n,m = 2,2 I can figure it out. But how do I figure out a general form for the isomorphism?
     
  5. Mar 14, 2007 #4

    StatusX

    User Avatar
    Homework Helper

    If there are two subgroups H and K of a group G such that the intersection of H and K is trivial and hk=kh for all h in H, k in K, then the subgroup HK is isomorphic to HxK.
     
  6. Mar 15, 2007 #5
    ah, thanks, I think I have it figured out now!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: How do I find an isomorphism between Sn+m and Zn x Zm?
  1. How do I do this? (Replies: 3)

  2. Polynomials in Zn[x] (Replies: 6)

Loading...