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!

Non-abelian subgroup of size 6 in A_6

  1. Oct 31, 2009 #1
    I need to find just one non-abelian subgroup of size 6 in A_6.

    I have started by noting that the subgroup must be isomorphic to D_6 and then tried to use the permutations in D_6 that sends corners to corners. I then came across the problem that the reflection elements in D_6 consist of 2-cycles and hence are not elements of A_6.
    I am now very stuck.... please help :)
     
  2. jcsd
  3. Oct 31, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    There's really only one nonabelian group of order 6, S_3. Can you think of a sort of natural way to find a copy of S_3 in A_6? Hint: interchange elements two at a time.
     
  4. Nov 1, 2009 #3
    Thanks a lot. I have found what the subgroup is now: {e, (23)(56), (13)(46), (12)(45), (123)(456), (132)(465)}. I need to justify my answer so I need to show that this is isomorphic to D_6 and therefore is a subgroup. I'll have a go.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Non-abelian subgroup of size 6 in A_6
Loading...