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Math Help - Semigroups: Do the following 4 equations imply x=y?

  1. #1
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    Semigroups: Do the following 4 equations imply x=y?

    xayxxa = xayxxayxya = yayxyaxyya = yaxyyaxyxa = xaxy
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  2. #2
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    Why didn't that post correctly?Equation 1: xayxxa = xayxEquation 2: xayxya = yayxEquation 3: yaxyya = yaxyEquation 4: yaxyxa = xaxy
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  3. #3
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by kiwijoey View Post
    Why didn't that post correctly?Equation 1: xayxxa = xayxEquation 2: xayxya = yayxEquation 3: yaxyya = yaxyEquation 4: yaxyxa = xaxy
    Well...no. Every relation is of the form u=v where |u| = 6 and |v|=4. As you are in a semigroup there is no way of getting a relation of the form u=v where |u|=1=|v| as you cannot cancel anything.

    What do you mean by the element a?
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