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Normal subgroup

  1. Oct 1, 2008 #1
    1. The problem statement, all variables and given/known data
    Let G be a group and let H,K be subgroups of G.
    Assume that H and K are Abelian. Let L=(H-union-K) be the subgroup of G generated by the set H-union-K. Show that H-intersect-K is a normal subgroup of L.



    3. The attempt at a solution
    How do i start this?
     
  2. jcsd
  3. Oct 1, 2008 #2

    morphism

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    Start by understanding the definition of L. Then it should be pretty obvious that H[itex]\cap[/itex]K is central in L.
     
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