FACPC-subgroup

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Definition

Suppose $G$ is a finite abelian group (i.e., a group that is both finite and abelian) and $H$ is a subgroup of $G$. We say that $H$ is a FACPC-subgroup or finite-abelian-characteristic-potentially characteristic subgroup of $G$ if there exists a finite abelian group $K$ containing $G$ such that both $H$ and $G$ are characteristic subgroups 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 finite abelian group

Weaker properties

property	quick description	proof of implication	proof of strictness (reverse implication failure)	intermediate notions
Subgroup of finite abelian group
Characteristic-potentially characteristic subgroup