Normal subgroup of finite group

This article describes a property that arises as the conjunction of a subgroup property: normal subgroup with a group property imposed on the ambient group: finite group
View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

Definition

A subgroup of a group is termed a normal subgroup of finite group if the whole group is a finite group and the subgroup is a normal subgroup of it.

Relation with other properties

Weaker properties

• Properties that ensure the subgroup is small:
  • Finite normal subgroup
  • Finitely generated normal subgroup
  • Normal closure of finite subset
• Properties that ensure the subgroup is not too far from the whole group:
  • Normal subgroup of finite index
• Normal subgroup in groups that are close to finite:
  • Normal subgroup of periodic group
  • Normal subgroup of finitely generated group
  • Normal subgroup of slender group