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Math Help - Abelian subgroup proof

  1. #1
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    Abelian subgroup proof

    If X, Y are subgroups of abelian group G, show XY={xy|xinX and yinY} is also subgroup of G.

    Would really appreciate some help with this.
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  2. #2
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    Quote Originally Posted by tamiani View Post
    If X, Y are subgroups of abelian group G, show XY={xy|xinX and yinY} is also subgroup of G.

    Would really appreciate some help with this.
    Remember how we prove a subgroup. We need to show a,b\in XY then ab \in XY. You also need to show e\in XY. Any if a\in XY then a^{-1} \in XY. Can you do these things? They should be straightforward.
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  3. #3
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    I thought that was it, but it seemed too simple. Thanks lots
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