On finite factorized groups with permutable subgroups of factors

Abstract

Two subgroups A and B of a group G are called msp-permutable if the following statements hold: AB is a subgroup of G; the subgroups P and Q are mutually permutable, where P is an arbitrary Sylow psubgroup of A and Q is an arbitrary Sylow q-subgroup of B, p ≠ q. In the present paper, we investigate groups that are factorized by two msppermutable subgroups. In particular, the supersolubility of the product of two supersoluble msp-permutable subgroups is proved.