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Quotient group

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Let G be a group, and R an equivalence relation compatible with the group structure on G. The structure derived from R on the quotient set G/R is called the quotient group of G by R, or the quotient group G/R, or G mod R.

An equivalence relation R(x,y) on G is compatible with the group structure on G if and only if it is equivalent to a relation of the form xy^{-1} \in H, for some normal subgroup H of G.

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