  Classes of algebraic structures that are defined by equational laws are
called varieties or equational classes. A variety is finitely generated if it
is defined by the laws that hold in some fixed finite algebra. We show that
every subvariety of a finitely generated congruence permutable variety is
finitely generated; in fact, we prove the more general result that if a
finitely generated variety has an edge term, then all its subvarieties are
finitely generated as well. This applies in particular to all varieties of
groups, loops, quasigroups and their expansions (e.g., modules, rings, Lie
algebras,...).
