On Hereditary Superradical Formations of Full Characteristic

A formation $\mathfrak{F}$ of finite groups is said to be superradical if it satisfies the following requirements:
$\bullet$ $\mathfrak{F}$ is a normally hereditary formation;
$\bullet$ any group $G=AB$, where $A$ and $B$ are $\mathfrak{F}$-subnormal $\mathfrak{F}$-subgroups in $G$, belongs to $\mathfrak{F}$.
The paper presents an infinite series of hereditary superradical formations of full characteristic that are not solvably saturated. This completes the negative answer to question 14.99 (b) in “Kourovka Notebook”.