Fully invariant subgroup of abelian group
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 |