1. Limited time only! Sign up for a free 30min personal 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!

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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Alternating Groups
  1. Alternatives to LaTek? (Replies: 2)

  2. Alternative to Rudin (Replies: 3)

Loading...