Laws of the lattices of foliated formations of \(T\)-groups
type: Item
instance of: scholarly article
title: Laws of the lattices of foliated formations of \(T\)-groups
zbMATH Open document ID: 1442.20008
author: Aleksandr Tsarev
publication date: 2019-11-29T00:00:00Z
review text: 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.
reviewed by: Danica Jakubiková-Studenovská
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D30
zbMATH DE Number: 7138894
zbMATH Keywords: multioperator \(T\)-group
zbMATH Keywords: \(\Omega _1\)-foliated formation
zbMATH Keywords: lattice of formations
zbMATH Keywords: modular lattice
zbMATH Keywords: \(T\)-subgroup functor
MaRDI profile type: Publication
full work available at URL: s12215-018-0369-3
OpenAlex ID: W2897881177
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DOI: 10.1007/S12215-018-0369-3
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 7138894