I'm studying group theory, and recently i read in a part that if we have a presentation $$\langle S | R \rangle$$ in wich in the right side we have an equation like $x=y$ that mean that we have a presentation in wich $y^{-1}x∊R$ That is true? if yes why $y^{-1}x∊R$ is the same that in the presented group $x=y$?
Meaning of equations in a presentation of a group
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$\begingroup$
group-theory
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0If you have a semigroup presentation (so you are not given an identity or inverses) then $R$ *must* consist of things of the form $x=y$. – 2012-05-29