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Thread: [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 $\displaystyle aH\subset Ha$, 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 $\displaystyle ah$ for some $\displaystyle h\in H$. And since $\displaystyle ah=ha$, ...
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  3. #3
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    Thanks Bruno, I figured it out.
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