Results 1 to 2 of 2

Thread: cycle

  1. #1
    Junior Member
    Joined
    May 2008
    Posts
    55

    Post cycle

    I have to show that if $\displaystyle sigma$ is a cycle of odd length then $\displaystyle sigma^2$ is a cycle.

    So this is what I assume, (and please help me check if it is an suitable answer);

    $\displaystyle wlog$, assume that
    $\displaystyle sigma=(1,2,3,......,m) where m is odd.$
    Because m is odd, I can compute that
    $\displaystyle sigma^2=(1,2,3,....,m)(1,2,3,....,m)(1,3,5,....,m, 2,4,6,...m-1) $
    which is again a cycle.
    Is this a suitable proof, and what else can I add to it.


    Thank You
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by Sally_Math View Post
    I have to show that if $\displaystyle sigma$ is a cycle of odd length then $\displaystyle sigma^2$ is a cycle.

    So this is what I assume, (and please help me check if it is an suitable answer);

    $\displaystyle wlog$, assume that
    $\displaystyle sigma=(1,2,3,......,m) where m is odd.$
    Because m is odd, I can compute that
    $\displaystyle sigma^2=(1,2,3,....,m)(1,2,3,....,m)=(1,3,5,....,m ,2,4,6,...m-1) $
    which is again a cycle.
    Is this a suitable proof, and what else can I add to it.


    Thank You
    I consider this proof to be fine. You can add by showing the the LHS and the RHS agree for all values of $\displaystyle 1,2,...,m$ in other words evaluating the LHS for any $\displaystyle 1,2,...,m$ will give the same result as RHS and so the two functions (bijections) are the same.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Order of a m-cycle
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: Oct 15th 2011, 10:01 PM
  2. [SOLVED] m cycle
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Oct 5th 2011, 12:25 AM
  3. cycle
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Apr 24th 2009, 09:37 AM
  4. cycle
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Feb 26th 2009, 04:26 PM
  5. Replies: 2
    Last Post: Dec 9th 2007, 03:33 PM

Search tags for this page

Click on a term to search for related topics.

Search Tags


/mathhelpforum @mathhelpforum