This article describes a property that arises as the conjunction of a subgroup property: characteristic 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
A subgroup of a group is termed a characteristic subgroup of finite group if it satisfies the following equivalent conditions:
- The whole group is a finite group and the subgroup is a characteristic subgroup of it.
- The whole group is a finite group and the subgroup is a strictly characteristic subgroup(i.e., invariant under all surjective endomorphisms) of it.
- The whole group is a finite group and the subgroup is an injective endomorphism-invariant subgroup of it.
Relation with other properties