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A4 subgroup question

  1. Apr 8, 2010 #1
    1. The problem statement, all variables and given/known data
    There is only one subgroup of order 4 in A4 (Alternating group of degree 4)(This subgroup is (1), (12)(34), (13)(24), (14)(23)). Why does this imply that this subgroup must be a normal subgroup in A4? Generalize to arbitrary finite groups.



    2. Relevant equations



    3. The attempt at a solution
    I thought about using the fact that for some g that is an element of a group G, |gH^-1g^-1|=|H| (the order of the subgroup H equals each of its conjugates orders) in the whole group, I am not sure were to go from here. Can some help me on this one at all?
     
  2. jcsd
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