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Homework Help: Abstract alg questions

  1. Dec 12, 2004 #1
    let G be a non-trivial group whose only supgroups are {e} and G. Show that G is cyclic of prime order.

    ok...so basically, it is asking I need show that it is cyclic that has an order that is only divisible by 1 and itself right?

    I dont know how to approace this, but I know the Fundamental Theorem of Cyclic groups, which says "Every subgroup of cyclic group is cyclic. So if the only subgroups are teh identity and itself, by the problem, doesn't that mean that it is prime order?

  2. jcsd
  3. Dec 12, 2004 #2


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    (a) Suppose it's not cyclic. What can you prove?
    (b) Suppose it's not of prime order. What can you prove?
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