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!

Conjugation of a permutation by a permutation in a permutation group

  1. Feb 17, 2008 #1
    1. The problem statement, all variables and given/known data
    Let n [tex]\geq[/tex]1. Let <a1,...,as> [tex]\in[/tex]Sn be a cycle and let [tex]\sigma[/tex][tex]\in[/tex]Sn be arbitrary. Show that

    [tex]\sigma\circ[/tex] <a1,...,as> [tex]\circ[/tex][tex]\sigma^{-1}[/tex] = <[tex]\sigma[/tex](a1),...,[tex]\sigma[/tex](as)> in Sn.



    2. Relevant equations



    3. The attempt at a solution
    As the title says, i believe this is a theorem regarding that the inverse permutation is the effect of a conjugation of a permutation by a permutation in a permutation group. Does anyone know a proof for this or where to find one?
     
  2. jcsd
  3. Feb 17, 2008 #2

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    That's pretty hard to read. It's usually better if you put adjacent things in one [tex] tag instead of several.
     
  4. Feb 18, 2008 #3
    Im sorry, here it is written in wikipedia simpler:

    One theorem regarding the inverse permutation is the effect of a conjugation of a permutation by a permutation in a permutation group. If we have a permutation Q=(i1 i2 … in) and a permutation P, then PQP−1 = (P(i1) P(i2) … P(in)).

    Please any help guys
     
  5. Feb 18, 2008 #4

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    Try it out with specific permutations and see if you can spot a general pattern.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Conjugation of a permutation by a permutation in a permutation group
  1. Permutation Group (Replies: 3)

  2. Permutation Groups (Replies: 3)

Loading...