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Math Help - groups

  1. #1
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    groups

    How to prove that in a group, the equations ax=b and ya=b are solvable for any a,b in G.
    Conversely how to show that any semigroup having this property contains a unit and is a group.
    Last edited by thomas_donald; August 29th 2009 at 06:08 PM.
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  2. #2
    ynj
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  3. #3
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    Thanks a lot!
    Can you help me on the first part:
    How to prove that in a group, the equations ax=b and ya=b are solvable for any a,b in G.
    Thanks again!
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  4. #4
    ynj
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    Quote Originally Posted by thomas_donald View Post
    Thanks a lot!
    Can you help me on the first part:
    How to prove that in a group, the equations ax=b and ya=b are solvable for any a,b in G.
    Thanks again!
    That is because ax=b\Leftrightarrow x=a^{-1}b,ya=b\Leftrightarrow y=ba^{-1}
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  5. #5
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    Thanks

    Thank you very much for your help.
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