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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


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    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..?
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