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Group Theory - specific non-abelian case

  1. May 8, 2009 #1
    1. The problem statement, all variables and given/known data

    Let G be an Abelian group and let H+{x^3 : x is an element of G}

    Find a non-Abelian group in which H is not a subgroup

    2. Relevant equations

    I wish it was that easy...

    3. The attempt at a solution

    I looked at the quaternion group, and some other matrix groups, but no luck so far...
     
  2. jcsd
  3. May 8, 2009 #2

    matt grime

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    What is the first non-abelian group in any reasonable ordering?
     
  4. May 8, 2009 #3
    The permutation group S_3.

    I looked at this also... but the cubes of the individual elements seemed closed under the operation of composition, and the identity is present... Four of us have spent about 3 hours on this without much luck, any nudging is greatly appreciated!
     
  5. May 8, 2009 #4
    You should triple-check your work, because matt is never wrong. If G=S_3, what are you thinking H is?
     
  6. May 8, 2009 #5
    Thanks for the help guys! I'm sure glad I don't have to take exams at midnight. A fresh set of eyes in the morning and your confirmation sure helped!
     
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