18.93 (2014)

Let $\mathfrak{M}$ be a one-generated saturated formation, that is, the intersection of all saturated formations containing some fixed finite group. Let $\mathfrak{F}$ be a subformation of $\mathfrak{M}$ such that $\mathfrak{F} \neq \mathfrak{F}\mathfrak{F}$.
$\qquad$ a) Is it true that then $\mathfrak{F}$ can be written in the form $\mathfrak{F} = \mathfrak{F}_1 \dots \mathfrak{F}_t$, where $\mathfrak{F}_i$ is a non-decomposable formation for every $i = 1, \dots, t$?
$\qquad$ b) Suppose that $\mathfrak{F} = \mathfrak{F}_1 \dots \mathfrak{F}_t$, where $\mathfrak{F}_i$ is a non-decomposable formation for every $i = 1, \dots, t$. Is it true that then all factors $\mathfrak{F}_i$ are uniquely determined?