Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A little problem with permutations.

  1. Aug 28, 2010 #1
    Let A_n be a subgroup of S_n that includes all the even permutations.


    How many permutations of order 6 does A_6 include?
     
    Last edited: Aug 28, 2010
  2. jcsd
  3. Aug 29, 2010 #2
    What do you mean by "order of a permutation"?
     
  4. Aug 30, 2010 #3
    The order of the permutation as an element of a group, of course.

    Remember that if you decompose an element x of Sn as a product of disjoint cycles, then the order of x is equal to the lcm of the lengths of the cycles. You will find that if you decompose an element x of S6 of order 6 into disjoint cycles, then x must be odd.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook