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

Subgroup of Sym(n)

  1. Aug 4, 2008 #1
    I need a proof of any subgroup of S_n which is isomorphic to S_(n-1) fixes a point in {1, 2,..., n} unless n=6.
  2. jcsd
  3. Aug 4, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    the standard answer: what have you tried?
  4. Aug 4, 2008 #3
    I defined a map psi: S_n to S_(n-1) and took a subgroup H={pi \in S_n | pi(n)=n}. And proved that H is a subgroup of S_n, but I want to prove that which is isomorphic to S_(n-1) and fixes a point in {1, 2..., } unless n=6.

    I thought to prove this

    If X is isomorphic to S_n and Y is isomorphic to X with |X:Y|=n then Y is isomorphic to S_(n-1).

    But still I don't know how to prove.
  5. Aug 4, 2008 #4
    No that second one is not correct.
  6. Aug 4, 2008 #5
    I should proof this

    If n \neq 6 then any subgroup Y of S_n with |S_n:Y|=n actually fixes a point..?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook