The result for metabelian groups yields an interesting consequence (see Dominions in product varieties, A. Magidin, Algebra Universalis, 43 (2-3) 217-232 (2000)):

   Theorem. Let Sn be the variety of all solvable groups of length at most n>1. Then there are non-trivial dominions in Sn.

   On the other hand, an argument of Susan McKay's implies that:

   Theorem. Let S be the category of all solvable groups (which is a pseudovariety but not a variety). Then all dominions are trivial in S.

   This should be compared with the situation in nilpotent groups, where the whole pseudovariety does have nontrivial dominions. In fact, the resilience of dominions here is almost non-existent. If G has length n, then for any m>n, the dominion of a subgroup H of G with respect to Sm will already be trivial. Again, compare with the situation for nilpotent groups, where a nilpotent groups of class two may have nontrivial dominions even in the whole pseudovariety.

   The subvarieties of Sn made up by restricting the exponent of the abelian groups whose extensions produce Sn will also have nontrivial dominions.