Abstract
We study the properties of finite groups in which every Sylow subgroup can be connected to the group by a chain of subgroups of prime indices. We establish the solubility of this type of groups. We prove that the class of all finite groups with this property of Sylow subgroups is a saturated hereditary formation. For these groups we find some analogs of the available theorems on the products of normal supersoluble subgroups.
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