Normal-potentially verbal subgroup

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Definition

A subgroup $H$ of a group $G$ is termed a normal-potentially verbal subgroup of $G$ if there exists a group $K$ containing $G$ as a normal subgroup such that $H$ is a verbal subgroup in $K$.

Relation with other properties

Stronger properties

property	quick description	proof of implication	proof of strictness (reverse implication failure)	intermediate notions
Verbal subgroup				|FULL LIST, MORE INFO
Central subgroup of finite group

Weaker properties

property	quick description	proof of implication	proof of strictness (reverse implication failure)	intermediate notions
Potentially verbal subgroup				|FULL LIST, MORE INFO
Potentially fully invariant subgroup
Normal-potentially fully invariant subgroup
Normal-potentially characteristic subgroup
Normal-extensible automorphism-invariant subgroup
Normal subgroup