Subnormal subgroup of finite group

This article describes a property that arises as the conjunction of a subgroup property: subnormal 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

Symbol-free definition

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

Relation with other properties

Stronger properties

• Normal subgroup of finite group

Weaker properties

• Finite subnormal subgroup
• Subnormal subgroup of finite index
• Join-transitively subnormal subgroup