Laws of the lattices of foliated formations of \(T\)-groups (Q2009783)

The paper deals with formations of \(T\)-groups. A formation is a class closed under taking homomorphic images and finite subdirect products. The notion of the partially foliated formation was introduced by Vedernikov; a basic idea lies in a constructing of new formations as satellites of various directions. The following theorem is proved: Let \(M\) be the class of all \(T\)-groups satisfying the minimality and maximality conditions for \(T\)-subgroups, and let \(n\) be a positive integer. Then every law of the lattice of all \(\tau\)-closed \(M\)-formations is fulfilled in the lattice of all \(\tau\)-closed \(n\)-multiply \(\Omega_1\)-foliated \(M\)-formations with direction \(\varphi\) such that \(\varphi_0\leq\varphi.\) Using this theorem, some corollaries and applications are deduced.