1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Permutation Group

  1. Sep 3, 2010 #1
    1. The problem statement, all variables and given/known data

    I have problems understanding part (f) of the following worked example:

    [PLAIN]http://img7.imageshack.us/img7/5557/61793282.gif [Broken]

    3. The attempt at a solution

    So in part (f), when calculating [tex](\sigma \tau)^{9000}[/tex], how does [tex](\sigma \tau)^{818 \times 11} (\sigma \tau)^2[/tex] reduce to [tex](\sigma \tau)^2[/tex]? What happens to the [tex](\sigma \tau)^{818 \times 11}[/tex] part?

    Similarly in [tex](\sigma \tau)^{-21}=(\sigma \tau)^{-2 \times 11} (\sigma \tau)^1 = (\sigma \tau)^1[/tex]

    why has the "[tex](\sigma \tau)^{-2 \times 11}[/tex]" been omitted?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 3, 2010 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    What is [tex](\sigma \tau)^11[/tex] equal to? Hint: You know that it has order 11
     
  4. Sep 6, 2010 #3
    Well, [tex](\sigma \tau)^{11}=e[/tex] where e is the identity. But what happens to the [tex](\sigma \tau)^{-2}[/tex]? Why does the "-2" disappear (since anything multiplied by the identity is itself)?
     
  5. Sep 6, 2010 #4

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    [tex](\sigma \tau)^{-2 \times 11} = ((\sigma \tau)^{11})^{-2}[/tex]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook