FACPC-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

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