2019
Том 71
№ 11

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

Abstract

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 and modular.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 4, pp 518-529.

Citation Example: Tsarev A. A., Vorob'ev N. N. On the modularity of a lattice of $τ$-closed $n$-ultiply $ω$-composite formations // Ukr. Mat. Zh. - 2010. - 62, № 4. - pp. 453–463.

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