By (Margolis et al., 2001, Proposition 2.9), G is in fact the only nontrivial extension-closed pseudovariety of groups that is LERF. On the other hand, it is easy to check that, for the pseudovariety Ab of all finite Abelian groups, every subgroup of [[OMEGA].sup.[kappa].sub.x] Ab is closed (Delgado, 1998, Proposition 3.8).
With same argument, we generalize this result to LERF pseudovarieties.
If V is a LERF pseudovariety of groups and [sigma] = k, then (4.2) holds for rational subsets L of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
You still go to Normandy and order a baguette by pulling your hands three feet apart and mumbling: "Erm, une of votre long lerfs
s'il vous plait." But at least you have the confidence to have a go.