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

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

xayxxa = xayxxayxya = yayxyaxyya = yaxyyaxyxa = xaxy

2. Why didn't that post correctly?Equation 1: xayxxa = xayxEquation 2: xayxya = yayxEquation 3: yaxyya = yaxyEquation 4: yaxyxa = xaxy

3. Originally Posted by kiwijoey
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 $a$?