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]

|Get subgroup property lookup help |Get exploration suggestions
VIEW RELATED: Subgroup property implications | Subgroup property non-implications | Subgroup metaproperty satisfactions | Subgroup metaproperty dissatisfactions | Subgroup property satisfactions |Subgroup property dissatisfactions
VIEW FACTS THAT:use, or start with, a subgroup satisfying the property|prove, or show that, a subgroup satisfies the property

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 normal closure in the whole group of a finitely generated subgroup.

Relation with other properties

Stronger properties

• Normal subgroup of finite group
• Finite normal subgroup
• Finitely generated normal subgroup

Weaker properties

• Normal subgroup