MATHEMATICS

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

I. K. Chirik

Gomel Engineering Institute of the Ministry for Emergency Situations of the Republic of Belarus, Gomel, Belarus

Abstract: 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.

Keywords: finite group, $p$-supersoluble group, $p$-solvable group.

UDC: 512.542

Received: 17.03.2014