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A ternary relation on a group

Start with your $x y^{-1} z x^{-1} y z^{-1} = 1$. Multiply both sides by $z$ from the right, then multiply both sides by $z^{-1}$ from the left. You get $z^{-1} x y^{-1} z x^{-1} y = 1$. In this way ...
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1 vote

A ternary relation on a group

Since $1=1^{-1}$ we have $(x y^{-1} z x^{-1} y z^{-1})^{-1} = zy^{-1}xz^{-1}yx^{-1} = 1$ which gives us $R(x,y,z)=R(z,y,x)$. With $x y^{-1} z x^{-1} y z^{-1} = 1$ we multiply on the left by $yz^{-1}$ ...
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