Normal closure of finite subset
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
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 normal closure in the whole group of a finitely generated subgroup.