CEP subgroup

In mathematics, in the field of group theory, a subgroup of a group is said to have the Congruence Extension Property or to be a CEP subgroup if every congruence on the subgroup lifts to a congruence of the whole group. Equivalently, every normal subgroup of the subgroup arises as the intersection with the subgroup of a normal subgroup of the whole group.
In symbols, a subgroup formula_1 is a CEP subgroup in a group formula_2 if every normal subgroup formula_3 of formula_1 can be realized as formula_5 where formula_6 is normal in formula_2.
The following facts are known about CEP subgroups: