On the structure of the smallest element of the Lockett section of a $\pi$-soluble fitting fu

Let f be a conjugate $\lambda$-normally embedded $\pi$-soluble Fitting functor and let $f_*$ be the smallest element of the Lockett section of f with respect to strong containment. A generalized version of an open question of Beidleman-Brewster-Hauck is to give a description of $f_*$. In this paper such a description is presented.