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

Order Problem

  1. Feb 17, 2007 #1
    Hey guys. Ive been stuck on the following thing for a little while now. Some help would be appreciated.

    If p divides o(G) (G an abelian group and p a prime), then show that
    G(p) = {g from G | o(g) = p^k for some k }

    I keep going round in circles.

    P.S. - this is not a homework question, just something I saw in an abstract algebra book that they stated without proof.
     
  2. jcsd
  3. Feb 17, 2007 #2
    What is G(p)? Are you sure this wasn't a definition?
     
  4. Feb 17, 2007 #3
    What about Cauchy's Theorem?
     
  5. Feb 18, 2007 #4

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    If you don't define G(p) for us we can't help. (The sylow p subgroup perhaps? but that is an easy exercise - all elements of order p^k lie in some sylow subgroup, and there is only one in an abelian group - so it must be something more difficult than that.)
     
    Last edited: Feb 18, 2007
  6. Feb 19, 2007 #5
    Did it:)

    Thanks to all who posted. My apologies for not defining G(p) properly. In any event, I solved the problem. The fundamental theorem of arithmetic did the trick (I underestimated the strength of the uniqueness of prime factorization in my earlier attempts!). Ciao
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Order Problem
  1. Order formula (Replies: 3)

  2. Order of elements (Replies: 4)

  3. Is order = size ? (Replies: 2)

  4. Order of element (Replies: 1)

Loading...