1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Permutations of a single number in the symmetric group

  1. Jan 3, 2013 #1
    Say we have the symmetric group [itex]S_5[/itex].

    The permutations of [itex]\{2,5\}[/itex] are the identity [itex]e[/itex] and the transposition [itex](25)[/itex].

    But what are all the permutations of [itex]\{3\}[/itex]? Is it [itex]e[/itex] and the 1-cycle [itex](3)[/itex]?
     
  2. jcsd
  3. Jan 3, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    What do you think would be the difference between e and (3)? Aren't they both the identity permutation?
     
  4. Jan 3, 2013 #3
    Oh yeah of course. You don't have to write 1-cycles in a permutation so [itex]e=(1)(2)(3)(4)(5)=(1)=(2)=(3)=(4)=(5)=(1)(2)=(1)(3)[/itex] etc.
     
  5. Jan 3, 2013 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Right. The number of permutations on n elements is n!. So for 2 elements you have two permutations, for 1 element you have one.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Permutations of a single number in the symmetric group
  1. Permutation Group (Replies: 25)

  2. Permutation Groups (Replies: 1)

  3. Permutation Group (Replies: 3)

  4. Permutation Groups (Replies: 3)

Loading...