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Alternating Groups

  1. Apr 5, 2009 #1
    Alternating groups apply to all even permutations in Sn for n > 2. Since n = 2 is inclusive, what got me wondering is that for such a case there are only 2 elements in S (say w and x); wouldn't that mean that the only transposition permutation would be (w x), which is an odd permutation?
     
  2. jcsd
  3. Apr 5, 2009 #2
    If you go by the fact that the order of any alternating group is [itex]n!/2[/itex] then you would have that the order of [itex]A_2[/itex] is [itex]2!/2=1[/itex] and therefore it's just the trivial group consisting of the identity element. Anything in the form of (wx) would be an odd permutation and therefore not in [itex]A_2[/itex]
     
  4. Apr 5, 2009 #3
    I see...so it would simply imply the identity element...Thanks
     
  5. Apr 5, 2009 #4
    No problem
     
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