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Permutation Group

  1. Apr 14, 2005 #1
    say you have the alternating group An for some permutation group Sn. If you are given An and then 1 odd permutation, must you be able to generate all of Sn? I tried it for S3 and I multiplied all the even perms in S3 by only 1 element that wasn't in A3 and was able to generate all of S3. Does this hold for any n?
     
    Last edited: Apr 14, 2005
  2. jcsd
  3. Apr 15, 2005 #2

    Galileo

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    Yes, that is generally true.
    Note that in any group multiplication on the left by an element in the group is a bijection.
    [tex]ax=b \iff x=a^{-1}b[/tex]
    Use this to prove it for the general case [itex]S_n ,n\geq 2[/itex]
    The case n=1 is special, since the A1=S1.
     
  4. Apr 15, 2005 #3
    Alright thanks a lot galileo. I just wanted to be sure of that fact before I brought it up in my presentation that I have to give.
     
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