Group commutator
= Group commutator
{title2=$[x,y]=x^{-1}y^{-1}xy$}
= Commutator of group elements
{synonym}
The <group commutator> measures the failure of two elements of a <group> to commute. Under the convention $[x,y]=x^{-1}y^{-1}xy$, it is the identity exactly when $xy=yx$. The <commutator subgroup> is generated by these elements. The alternative convention $xyx^{-1}y^{-1}$ generates the same <commutator subgroup>; individual formulas must specify their convention.