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Math Help - Normal subgroups of a group

  1. #1
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    Normal subgroups of a group

    I have two normal subgroups (call them X and Y) of a group with only the identity element in common and need to show that xy = yx for all x \in X, y \in Y.

    I really have no idea where to begin although I do understand the definition of a normal subgroup. I think that gxyg^-1 is in XY but am not sure what this means, whether or not XY is a normal subgroup or whether I am meant to look for a homomorphism or isomorphism.

    Any help appreciated, thanks.
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  2. #2
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    Opalg's Avatar
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    Notice that the element x(yx^{-1}y^{-1}) =(xyx^{-1})y^{-1} is in both X and Y (why?) and must therefore be the identity element.
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