The lattices of n-multiply Ω1-foliated τ-closed formations of multioperator T -groups

Abstract

In this paper, it is shown that the lattice 1 F ' n of all n-multiply 1 -foliated -closed M-formations with direction ', ' 0 ', for any n 2 N 0 is algebraic, modular, and complete in M, where M is the class of all multioperator T -groups satisfying the minimality and maximality conditions for T -subgroups. We give a complete description of n-multiply 1 -foliated -closed M-formations F with l ‚ .F/ 2, where ‚ D 1 F ' n , n 2 N 0 , and ' 0 '. We also investigate n-multiply 1 -foliated -closed M-formations with r-direction ' such that '.A/ M A 0 M A for all A 2 I 1 for which the lattice of all n-multiply 1 -foliated -closed M-formations with direction ' is Boolean.