Results 1 to 2 of 2

Math Help - Group with prime order?

  1. #1
    Junior Member
    Joined
    Jun 2010
    Posts
    27

    Group with prime order?

    Hi guys,

    I've been asked to prove the following:
    Prove that every group whose order is a power of a prime p contains an element of order p.


    This is the proof I've come up with. I feel like it is really long and contrived. The only tools that I have at my disposal is LaGrange's Theorem and the associated corollaries.




    Uploaded with ImageShack.us
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by CropDuster View Post
    Hi guys,

    I've been asked to prove the following:
    Prove that every group whose order is a power of a prime p contains an element of order p.


    This is the proof I've come up with. I feel like it is really long and contrived. The only tools that I have at my disposal is LaGrange's Theorem and the associated corollaries.




    Uploaded with ImageShack.us

    I think the above is too long. Immediately after "assume |<x>|\neq p " you can finish swiftly: then

    |<x>|=p^m\Longrightarrow which means ord(x)=p^m\Longrightarrow ord(x^{p^{m-1}})=p and we're done.

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: March 1st 2011, 07:39 PM
  2. Replies: 3
    Last Post: February 17th 2011, 08:51 AM
  3. Show only one group exists for Groups of prime order
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: May 30th 2010, 03:52 PM
  4. Group order prime, center, abelian
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 13th 2008, 06:31 PM
  5. Finite group with element of prime order
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: September 8th 2007, 05:51 PM

Search Tags


/mathhelpforum @mathhelpforum