Abelian-potentially verbal 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 an abelian-potentially verbal subgroup if there exists an abelian group K containing G such that H is a verbal subgroup of K.

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 |FULL LIST, MORE INFO
Subgroup of finite abelian group |FULL LIST, MORE INFO

Weaker properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions
Abelian-potentially fully invariant subgroup fully invariant not implies abelian-potentially verbal
Abelian-potentially characteristic subgroup
Subgroup of abelian group