Group Theory - specific non-abelian case

[audiowize]

Homework Statement

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

Homework Equations

I wish it was that easy...

The Attempt at a Solution

I looked at the quaternion group, and some other matrix groups, but no luck so far...

 

[matt grime]

What is the first non-abelian group in any reasonable ordering?

 

[audiowize]

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!

 

[Billy Bob]

You should triple-check your work, because matt is never wrong. If G=S_3, what are you thinking H is?

 

[audiowize]

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!