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Math Help - What's the correct converse of this problem?

  1. #1
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    What's the correct converse of this problem?

    What's the correct converse of this problem?-capture.png

    Which is the correct converse for the pictured question (so you can see the exact wording)?

    Converse One: Take the converse of the statement agb=cgd always implies that ab=cd. That is:

    Suppose G is a group with the property that ab=cd always implies agb=cgd. Prove or disprove G is abelian.

    This seems like a kind of silly statement, and I see no way to prove it. The only way to make ab=cd is if a=c and b=d or if a=b=c=d.

    Converse Two: Take the converse of the question. That is:

    Suppose that G is an abelian group. Prove that G has the property that agb=cgd always implies ab=cd.

    Which is too easy to be part (b) of this question. If G is abelian and agb=cgd, then we have
    agb=cgd
    gab=gcd
    g-1gab=g-1gcd
    ab=cd


    Which means that G has that property.
    TIA.
    Last edited by MSUMathStdnt; January 26th 2013 at 10:11 PM.
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  2. #2
    MHF Contributor

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    Re: What's the correct converse of this problem?

    the wording of the question is vague, and i understand your confusion. however, i favor your "converse two" as the correct one.
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