 For example, a group is an algebraic object consisting of a set together with a single binary operation, satisfying certain axioms.If formula_29 is a group with operation formula_30, a congruence relation on formula_29 is an equivalence relation formula_32 on the elements of formula_29 satisfying
for all formula_36, formula_37, formula_38, formula_39.For a congruence on a group, the equivalence class containing the identity element is always a normal subgroup, and the other equivalence classes are the cosets of this subgroup.