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Normal subgroups of a non-albelian group

  1. Dec 18, 2008 #1
    I have the table for a non-albelian group. I know the subgroups of this group. I need to know which subgroups are normal. How can I tell?
     
  2. jcsd
  3. Dec 19, 2008 #2
  4. Dec 19, 2008 #3
    So you need to check every single entry?
     
  5. Dec 19, 2008 #4
    Well some of these groups will be infinite so that's impossible but for finite groups I guess it would work but would be a tad tedious. We're looking for a more generic proof.

    Consider the following,
    Let [itex] H \subset G [/itex]. The group [itex] G [/itex] is abelian and therefore has commutivity of elements by design i.e.
    [itex] ah=ha [/itex]
    However, this holds [itex]\forall h \in H [/itex] and [itex] \forall a \in G [/itex]
    [itex] \Rightarrow aH=Ha \Rightarrow a^{-1}aH=a^{-1}Ha [/itex]
    [itex] a^{-1}Ha=H [/itex]
     
  6. Dec 19, 2008 #5
    But my group isn't abelian.
     
  7. Dec 19, 2008 #6
    haha i am being silly...let me reconsider
     
  8. Dec 19, 2008 #7
    could u post the question?
     
  9. Dec 19, 2008 #8
    It's for a take-home final so I'm trying to ask for help on the concepts without doing that. I'll post it after I turn it in.
     
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