Nilpotent variety of groups

Definition

A nilpotent variety of groups is a subvariety of the variety of groups (i.e., a collection of groups closed under taking subgroups, quotients, and direct products) satisfying the following equivalent conditions:

1. Every group in it is nilpotent
2. There exists a nonnegative integer $c$ such that every group in the collection is nilpotent with nilpotency class at most $c$

Equivalence of definitions

For full proof, refer: Equivalence of definitions of nilpotent variety