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Show G is cyclic

  1. Mar 15, 2012 #1
    1. Let p be a prime and G a group whose order is p. Prove that G is cyclic.

    2. I know that if p is prime, then the only possible subgroups of G are {e} and G itself. But, how to use this fact to show that G is cyclic?
  2. jcsd
  3. Mar 15, 2012 #2


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    Pick an element g of G that is not e and consider the subgroup generated by g.
  4. Mar 15, 2012 #3
    HINT: Lagrange
    Last edited: Mar 15, 2012
  5. Mar 15, 2012 #4
    Ok, this may sound stupid, but, how do I know that <g>=G?
  6. Mar 15, 2012 #5
    Oh, wait, there are only two subgroups,so it has to be.

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