18.9 (2014)

Does there exist a subgroup-closed saturated formation $\mathfrak{F}$ of finite groups properly contained in $\mathfrak{E}_\pi$, where $\pi = \text{char}(\mathfrak{F})$, satisfying the following property: if $G \in \mathfrak{F}$, then there exists a prime $p$ (depending on the group $G$) such that the wreath product $C_p \wr G$ belongs to $\mathfrak{F}$, where $C_p$ is the cyclic group of order $p$?