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Math Help - [SOLVED] Proving subgroups

  1. #1
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    [SOLVED] Proving subgroups

    Hey guys,

    I am stuck on the following problem:

    If C is a subgroup of an abelian group G, then a*H = H*a for all a in G.

    I know that I have to prove

    1.) a*H is a subset of H*a

    2.) H*a is a subset of a*H

    After this, I really don't know how to go about it. Thanks for any and all help.
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    To show that aH\subset Ha, take any element on the left side and show that it's also an element of the right side. An element of the left side is ah for some h\in H. And since ah=ha, ...
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  3. #3
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    Thanks Bruno, I figured it out.
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