Proof: symmetric group is not cyclic

Discussion in 'Undergraduate Math' started by Linda Pan, Sep 16, 2003.

  1. Linda Pan

    Linda Pan Guest

    Hi,

    I have two ways to prove symmetric group is not cyclic if n is more than 2.
    I'd like to listen to your ideas about my proofs. Thanks.

    1)
    Since symmetric group is not abelian (n>2),
    and cyclic group is abelian,
    so, symmetric group is not cyclic group (n>2)

    2)
    Since symmetric group is a permutation group of order n!,
    and cyclic group only has order n,
    so, when n>2, symmetric group is not cyclic.

    Please give your suggestion. Thanks again.

    P.L.
     
    Linda Pan, Sep 16, 2003
    #1
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  2. This one is correct (assuming you have proven that S_n is nonabelian
    when n>2).
    This one is hopelessly wrong. Why could the symmetric group not be
    cyclic of order n!?

    ======================================================================
    "It's not denial. I'm just very selective about
    what I accept as reality."
    --- Calvin ("Calvin and Hobbes")
    ======================================================================

    Arturo Magidin
     
    Arturo Magidin, Sep 16, 2003
    #2
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