The p-length bound for mutually permutable products of p-solvable groups

Let $G=AB$ be a mutually permutable product of two $p$-solvable subgroups $A$ and $B$, where $p\in\pi(G)$. Write $l_p(G)$ for the $p$-length of $G$, and let $\tau_p(A)$ and $\tau_p(B)$ denote the corresponding Sylow-number parameters for $A$ and $B$. The $p$-length conjecture. Then

$$l_p(G)\leq \max\left\{1+\frac{\tau_p(A)}{2},1+\frac{\tau_p(B)}{2}\right\}.$$

The paper asks whether either of the additional hypotheses in the preceding theorem—$(|G|,p-1)=1$ or one of $A$ and $B$ being $p$-nilpotent—can be removed. The conjecture is therefore presented as the unrestricted extension of that theorem; its status is not resolved in the supplied text.