Results 1 to 2 of 2

Math Help - Finite group with element of prime order

  1. #1
    Newbie
    Joined
    Feb 2013
    From
    United States
    Posts
    1

    Finite group with element of prime order

    I have this problem due this Thursday, and I used a solution on here to help me figure it out. The problem is this: "Let G be a non-trivial finite group. Prove that G contains an element of prime order." I have solved the proof, but have a little trouble understanding the explanation from the solution I found, which my professor noticed. His comment towards my solution was this: "In the sentence beginning "Then, suppose (there exists) q in Z ...", what are you trying to say? Of course if q<p then mq<mp, but what does that matter? What would that contradict?" I understand that this new finding contradicts the definition of the order of the element, but I don't know how to further explain this in my proof. Any help would be appreciated as soon as possible. Thanks!
    Attached Thumbnails Attached Thumbnails Finite group with element of prime order-exam1-presentation-problem.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member jakncoke's Avatar
    Joined
    May 2010
    Posts
    387
    Thanks
    80

    Re: Finite group with element of prime order

    I'm not sure what you meant to do. You coulda have just used the fundamental theorem of arithmetic.

    If n is a prime, it has a unique prime decomopsition n = p_1..p_n a^{n} = a^{{p_i...p_n}^{p_1}} = e, since each p_i..p_n \leq n, a^{p_i...p_n} is indeed an element of prime order p_1
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: November 9th 2012, 10:12 AM
  2. Replies: 3
    Last Post: February 17th 2011, 08:51 AM
  3. Replies: 1
    Last Post: November 5th 2009, 07:14 PM
  4. Replies: 5
    Last Post: September 6th 2009, 08:29 AM
  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