1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    (a) Suppose it's not cyclic. What can you prove?
    (b) Suppose it's not of prime order. What can you prove?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Abstract alg questions
  1. Abstract Algebra (Replies: 35)