Fully invariant subgroup of abelian group

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This article describes a property that arises as the conjunction of a subgroup property: fully invariant subgroup with a group property imposed on the ambient group: abelian 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 fully invariant subgroup of abelian group is a fully invariant subgroup of an abelian group, i.e., a subgroup of abelian group that is invariant under all the endomorphisms of the whole group.

Relation with other properties

Stronger properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions
Verbal subgroup of abelian group

Weaker properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions
Characteristic subgroup of abelian group
Abelian-extensible endomorphism-invariant subgroup
Abelian-quotient-pullbackable endomorphism-invariant subgroup
Subgroup of abelian group