Proof: symmetric group is not cyclic

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

  1. Linda Pan

    Linda Pan Guest


    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.

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

    Linda Pan, Sep 16, 2003
    1. Advertisements

  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
    1. Advertisements

Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.