Solvable variety of groups

Definition

A solvable variety of groups or soluble 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 the variety is solvable.
2. There exists a nonnegative integer $c$ such that every group in the variety is solvable with solvable length at most $c$.

Equivalence of definitions

Further information: Equivalence of definitions of solvable variety