The subgroups $A$ and $B$ of a group~$G$ are called { \rm 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 $p$-subgroup of~$A$ and $Q$~is an arbitrary Sylow $q$-subgroup of~$B$, ${ p\neq q}$. In the present paper, we investigate groups that factorized by two { \rm msp}-permutable subgroups. In particular, the supersolubility of the product of two supersoluble { \rm msp}-permutable subgroups is proved.
Categories: math.GR