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Basic group theory problem

  1. May 22, 2014 #1
    Let H be a normal subgroup of G. Then factor group G/H is an abelian subgroup.
    For x, y not in H
    xHyH=yHxH
    and xyH=yxH
    (xyH)(yxH)^{-1}=id
    xyx^{-1}y^{-1}=id

    Are these steps correct?


    thnx
     
  2. jcsd
  3. May 22, 2014 #2
    Are you trying to prove this?

    What happens if ##H=\{e\}##?

    Also, the factor group ##G/H## is not a subgroup of ##G##.
     
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