On certain properties of totally local formations

$l_\infty\operatorname{form}G$
The structure of the totally local formation $l_\infty\operatorname{form}G$, generated by a simple non-Abelian group $G$ is described. By applying this result we prove the existence of totally local formations that are not idempotents of the semigroup $G_\infty$ of all totally local formations and are not representable as the product of finitely many indecomposable elements of $G_\infty$. We also describe totally local formations all of whose totally local subformations are hereditary.