• Support PF! Buy your school textbooks, materials and every day products Here!

Group Theory - specific non-abelian case

  • Thread starter audiowize
  • Start date
  • #1
7
0

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...
 

Answers and Replies

  • #2
matt grime
Science Advisor
Homework Helper
9,395
3
What is the first non-abelian group in any reasonable ordering?
 
  • #3
7
0
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!
 
  • #4
392
0
You should triple-check your work, because matt is never wrong. If G=S_3, what are you thinking H is?
 
  • #5
7
0
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!
 

Related Threads for: Group Theory - specific non-abelian case

  • Last Post
2
Replies
38
Views
1K
  • Last Post
Replies
0
Views
4K
Replies
8
Views
9K
Replies
7
Views
3K
Replies
3
Views
339
Replies
12
Views
3K
Replies
4
Views
4K
Replies
6
Views
10K
Top