On the modularity of a lattice of $τ$-closed $n$-ultiply $ω$-composite formations

• Date: 2010
• Main Authors: Vorob'ev, N. N., Tsarev, A. A., Воробьев, Н. Н., Царёв, A. A.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2010
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2879
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $n ≥ 0$, let $ω$ be a nonempty set of prime numbers and let $τ$ be a subgroup functor (in Skiba’s sense) such that all subgroups of any finite group $G$ contained in $τ (G)$ are subnormal in $G$. It is shown that the lattice of all $τ$-closed $n$-multiply $ω$-composite formations is algebraic an...