Normal closure of finite subset

Definition
A subgroup of a group is termed a normal closure of finite subset if there is a finite subset of that subgroup such that the normal subgroup generated by that finite subset in the whole group is the subgroup. In other words, the subgroup arises as the defining ingredient::normal closure in the whole group of a finitely generated subgroup.

Stronger properties

 * Weaker than::Normal subgroup of finite group
 * Weaker than::Finite normal subgroup
 * Weaker than::Finitely generated normal subgroup

Weaker properties

 * Stronger than::Normal subgroup