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 H is a CEP subgroup in a group G if every normal subgroup N of H can be realized as H ∩ M where M is normal in G .

The following facts are known about CEP subgroups: