MATHEMATICS

Elements of the height 3 of the lattice of all $\tau$-closed $n$-multiply $\omega$-composition formations

P. A. Zhiznevsky

F. Skorina Gomel State University, Gomel

Abstract: In this paper elements of the height 3 of the lattice $ c^{\tau}_{\omega_n}$ of all $\tau$-closed $n$-multiply $\omega$-composition formations are described. It is proved that if $\mathfrak{F}$ is an element of the height 3 of the lattice $ c^{\tau}_{\omega_n}$, then the lattice of $\tau$-closed $n$-multiply $\omega$-composition subformations of $\mathfrak{F}$ is distributive.

Keywords: finite group, formation, $\omega$-composition satellite, $\tau$-closed $n$-multiply $\omega$-composition formation, height of formation.

UDC: 512.542.6

Received: 26.05.2011