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Homework Help: Normal subgroup

  1. May 16, 2012 #1
    H=A3= {(1),(1 2 3),(1 3 2)} and

    G=S3 ={ (1),(1 2 3),(1 3 2),(1 2 ),(1 3),(1 2 3) }

    Is H is normal subgroup of G ?
    I try g=(1 2 3 ) for gH=Hg but gH≠Hg for all g ε G.In this situation,H is normal subgroup pf G?
     
  2. jcsd
  3. May 18, 2012 #2
    I haven't check your assertion, but in order for H to be a normal subgroup of G, ##gH = Hg## for all ##g\in G##.

    If you have ##gH\neq Hg## for some ##g\in G##, then H isn't a normal subgroup of G.
     
  4. May 18, 2012 #3
    What is [G:H]?? What does that tell you??
     
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