7.38 (1980)

A variety of profinite groups is a non-empty class of profinite groups closed under taking subgroups, factor-groups, and Tikhonov products. A subvariety $\mathfrak{V}$ of the variety $\mathfrak{N}$ of all pronilpotent groups is said to be (locally) nilpotent if all (finitely generated) groups in $\mathfrak{V}$ are nilpotent.
$\qquad$ a) Is it true that any non-nilpotent subvariety of $\mathfrak{N}$ contains a non-nilpotent locally nilpotent subvariety?
$\qquad$ b) The same problem for the variety of all pro-$p$-groups (for a given prime $p$).