On $p$-supersolubility of a finite factorized group with prime indexes of factors

Sufficient conditions for $p$-supersolubility of a finite group $G=AB$, where $A$ and $B$ have cyclic Sylow $p$-subgroups are received. In particular, the supersolubility of a finite group $G=AB$ providing that all Sylow subgroups of $A$ and $B$ arecyclic, and the indexes of $A$ and $B$ in the group $G$ are prime is proved.