Results 1 to 2 of 2

Thread: Finding element of maximal order in symmetric group

  1. #1
    Member
    Joined
    Nov 2008
    Posts
    76

    Finding element of maximal order in symmetric group

    Would someone show me the method to find an element of maximal order in $\displaystyle S_7$? Is there a general technique for this?
    I think that this element could have order 12=3 $\displaystyle \times$4 since I can find a (4,3) cycle element in $\displaystyle S_7$ like (1234)(567) which has order 12.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by jackie View Post
    Would someone show me the method to find an element of maximal order in $\displaystyle S_7$? Is there a general technique for this?
    I think that this element could have order 12=3 $\displaystyle \times$4 since I can find a (4,3) cycle element in $\displaystyle S_7$ like (1234)(567) which has order 12.
    $\displaystyle 12$ is the answer. if there exists an integer $\displaystyle m=p_1^{k_1}p_2^{k_2} \cdots p_r^{k_r},$ where $\displaystyle p_1, \cdots, p_r$ are distinct primes, such that $\displaystyle p_1^{k_1} + p_2^{k_2} + \cdots + p_r^{k_r} = n,$ then the maximal order of elements in $\displaystyle S_n$ is $\displaystyle m.$

    for example, since $\displaystyle 12=2^2 \times 3$ and $\displaystyle 2^2 + 3 = 7,$ the maximal order of elements in $\displaystyle S_7$ is $\displaystyle 12.$

    see section 4 (the prime connection) of this paper for more details. don't get scared, it's very easy to understand!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. order of an element of a group
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: Apr 30th 2010, 12:55 PM
  2. Finding the order of a group element
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: Nov 13th 2009, 07:48 AM
  3. A partial order set with a non-unique maximal element
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: Aug 29th 2009, 07:57 AM
  4. 4th symmetric group, order
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Jun 12th 2009, 12:30 AM
  5. group element order
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 1st 2009, 07:23 AM

Search Tags


/mathhelpforum @mathhelpforum