Let G {\displaystyle {}G} be a group, and let H ⊆ G {\displaystyle {}H\subseteq G} be a subgroup. We set x ∼ H y {\displaystyle {}x\sim _{H}y} (and say that x {\displaystyle {}x} and y {\displaystyle {}y} are equivalent) if x − 1 y ∈ H {\displaystyle {}x^{-1}y\in H} .
