18.92 (2014)

A non-empty set $\theta$ of formations is called a complete lattice of formations if the intersection of any set of formations in $\theta$ belongs to $\theta$ and $\theta$ has the largest element (with respect to inclusion). If $L$ is a complete lattice, then an element $a \in L$ is said to be compact if $a \leqslant \bigvee X$ for any $X \subseteq L$ implies that $a \leqslant \bigvee X_1$ for some finite $X_1 \subset X$. A complete lattice is called algebraic if every element is the join of a (possibly infinite) set of compact elements.
$\qquad$ a) Is there a non-algebraic complete lattice of formations of finite groups?
$\qquad$ b) Is there a non-modular complete lattice of formations of finite groups?