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Groupprops β

Fully invariant subgroup of abelian group

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