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!

Group theory

  1. May 30, 2007 #1
    1. The problem statement, all variables and given/known data

    Prove that [tex]Aut(S_3)=S_3[/tex]
    2. Relevant equations
    = means isomorphic

    3. The attempt at a solution

    If I let [tex]S_3[/tex] be {1,2,3} then I can write out explicitly its 6 elements...the permutations of 1,2,3...
    Aut(S3) is the set of isomorphisms of S3 onto itself. So can I just write them all out and then say that since they have the same order they are isomorphic?
    Or is there a better way?

  2. jcsd
  3. May 30, 2007 #2


    User Avatar
    Homework Helper

    If you can show there are exactly 6 isomorphisms, then you've shown Aut(S_3) is one of the two groups of order 6: Z_6 and S_3. These can be distinguished by the fact that Z_6 is abelian while S_3 is not, so it only remains to find a pair of isomorphisms that don't commute.

    How were you planning on showing there are exactly 6 isomorphisms? If you're not sure here, think about the relation:

  4. May 31, 2007 #3

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    No. This does not prove anything.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Group theory
  1. Group Theory (Replies: 2)

  2. Group Theory (Replies: 1)

  3. Group Theory (Replies: 16)

  4. Group Theory (Replies: 1)

  5. Group theory (Replies: 1)