Abelian-potentially characteristic subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

A subgroup H of an abelian group G is termed an abelian-potentially characteristic subgroup if there exists an abelian group K containing G such that H is a characteristic subgroup of K.

Relation with other properties

Stronger properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions
Characteristic subgroup of abelian group characteristic subgroup of abelian group direct from definition abelian-potentially characteristic not implies characteristic |FULL LIST, MORE INFO
Abelian-potentially fully invariant subgroup is a fully invariant subgroup in some bigger abelian group follows from fully invariant implies characteristic  ? |FULL LIST, MORE INFO
Abelian-potentially verbal subgroup is a verbal subgroup in some bigger abelian group |FULL LIST, MORE INFO
Subgroup of finite abelian group finite abelian NPC theorem Abelian-potentially verbal subgroup|FULL LIST, MORE INFO

Weaker properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions
Abelian-extensible automorphism-invariant subgroup invariant under all abelian-extensible automorphisms abelian-potentially characteristic implies abelian-extensible automorphism-invariant  ? |FULL LIST, MORE INFO
Subgroup of abelian group subgroup of an abelian group Abelian-extensible automorphism-invariant subgroup|FULL LIST, MORE INFO