On finite groups whose Sylow subgroups are submodular

Abstract: A subgroup $H$ of a finite group $G$ is called submodular in $G$, if we can connect $H$ with $G$ by a chain of subgroups, each of which is modular (in the sense of Kurosh) in the next. If a group $G$ is supersoluble and every Sylow subgroup of $G$ is submodular in $G$, then $G$ is called strongly supersoluble. The properties of groups with submodular Sylow subgroups are obtained. In particular, we proved that in a group every Sylow subgroup is submodular if and only if the group is Ore dispersive and every its biprimary subgroup is strongly supersoluble.