Finite-potentially verbal subgroup

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Definition

Definition with symbols

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

Relation with other properties

Stronger properties

• Central subgroup of finite group: For full proof, refer: Central implies potentially verbal in finite
• Cyclic normal subgroup of finite group (cyclic normal subgroup of finite group): For full proof, refer: Cyclic normal implies potentially verbal in finite
• Finite-pi-potentially verbal subgroup