Factorization of One-Generated Formations

A large class of one-generated factorable foliated formations including composition, bicanonical, and other formations is described. V. A. Vedernikov suggested to study foliated formations with directions $\beta$ such that $\alpha\le\beta\le\gamma$, where $\alpha$ and $\gamma$ are also some directions, from a unified point of view. We study one-generated factorable foliated formations with directions from the interval $[\alpha,\gamma]$, where $\alpha$ and $\gamma$ are the directions of the bicanonical and composition formations, respectively. In particular, all irreducible factorizations of one-generated composition formations are studied.