Results 1 to 2 of 2

Math Help - Order of a Group, Order of an Element

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    128

    Order of a Group, Order of an Element

    Hello,

    I am trying to prove that a group of order 12 must have an element of order 2.

    I have a feeling this is a consequence of Lagrange's theorem.... although I am not sure how so.

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by matt.qmar View Post
    Hello,

    I am trying to prove that a group of order 12 must have an element of order 2.

    I have a feeling this is a consequence of Lagrange's theorem.... although I am not sure how so.

    Thanks

    The order of an element in a group of order 12 can be 1,2,3,4,6,or 12: the only element of order 1 is the unit, if a\in G has

    order 12 then a^6 has order 2, and similarly if it has order 6 or 4 we get an element of order 2.

    The only possibility left thus is that all the non-unit elements of G have order 3, but if we try to pair each element with its

    unique inverse then we've a problem....take it from here.

    Tonio

    Ps. Of course, if you already know Cauchy's Theorem or the Sylow theorems the problem is trivial, so I assume you don't.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. element of order II, in 2n order group
    Posted in the Advanced Algebra Forum
    Replies: 14
    Last Post: December 14th 2011, 09:32 AM
  2. Replies: 3
    Last Post: February 17th 2011, 07:51 AM
  3. Order of a Group, Order of an Element
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: November 15th 2010, 06:02 PM
  4. order of an element of a group
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: April 30th 2010, 12:55 PM
  5. group element order
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 1st 2009, 07:23 AM

Search Tags


/mathhelpforum @mathhelpforum