14.78 (1999)

Suppose that $\mathfrak{H} \subseteq \mathfrak{F}_1 \subseteq \mathfrak{M}$ and $\mathfrak{H} \subseteq \mathfrak{F}_2 \subseteq \mathfrak{M}$ where $\mathfrak{H}$ and $\mathfrak{M}$ are local formations of finite groups and $\mathfrak{F}_1$ is a complement for $\mathfrak{F}_2$ in the lattice of all formations between $\mathfrak{H}$ and $\mathfrak{M}$. Is it true that $\mathfrak{F}_1$ and $\mathfrak{F}_2$ are local formations? This is true in the case $\mathfrak{H} = (1)$.