Lattices of composition formations of finite groups and the laws

Abstract

We prove that every law of the lattice of all τ-closed formations of finite groups is fulfilled in the lattice of all τ-closed n-multiply ω-composition formations of finite groups for every non-empty set of primes ω and every non-negative integer n. Let n ≥ 0 and ω be an infinite set of primes. It is proved that the lattice of all τ-closed n-multiply ω-composition formations is not distributive.