Variety-dominating subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed variety-dominating if there exists a subvariety $$\mathcal{V}$$ of the variety of groups such that:


 * $$H \in \mathcal{V}$$.
 * If $$K \le G$$ is such that $$K \in \mathcal{V}$$, there exists $$g \in G$$ such that $$gKg^{-1} \le H$$.

Stronger properties

 * Weaker than::Variety-containing subgroup

Weaker properties

 * Stronger than::Homomorph-dominating subgroup

Facts

 * Variety-dominating in finite iff order-dominating Hall