Schur-Baer variety

Definition
A Schur-Baer variety is a subvariety of the variety of groups with the following equivalent conditions:


 * 1) For any group $$G$$ such that the quotient group of $$G$$ by its marginal subgroup corresponding to that subvariety is a finite group, it is also true that the verbal subgroup corresponding to that variety is a finite group, and its order divides a power of the order of the quotient by the marginal subgroup.
 * 2) For any finite group $$G$$, the defining ingredient::Baer invariant $$\mathcal{V}M(G)$$ is also a finite group and its order divides a power of the order of $$G$$ (i.e., all prime factors of its order are also prime factors of the order of $$G$$).

Facts

 * Schur-Baer theorem states that the variety of abelian groups is a Schur-Baer variety.