On a lattice characterization of finite soluble $PST$-groups

Zhang Chi, Alexander N. Skiba

Let $\mathfrak{F}$ be a class of finite groups and $G$ a finite group. Let ${\mathcal{L}}_{\mathfrak{F}}(G)$ be the set of all subgroups $A$ of $G$ with $A^G/A_G\in \mathfrak{F}$. A…