On algebraicity of lattices of $\omega$-fibred formations of finite groups
Diskretnaya Matematika, Tome 34 (2022) no. 1, pp. 23-35
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For a nonempty set $\omega$ of primes, V. A. Vedernikov had
constructed $\omega$-fibred formations of groups via function methods.
We study lattice properties of $\omega$-fibred formations of finite groups with direction $\delta$
satisfying the condition $\delta_{_{0}} \leq \delta$.
The lattice $\omega\delta F_{\theta}$ of all $\omega$-fibred formations with direction $\delta$ and $\theta$-valued
$\omega$-satellite is shown to be algebraic under the condition that the lattice of formations $\theta$ is algebraic.
As a corollary,
the lattices $\omega\delta F$,
$\omega\delta F_{\tau}$, $\tau\omega\delta F$,
$\omega\delta^{n} F$ of $\omega$-fibred formations of groups are shown to be algebraic.
Keywords:
finite group, class of groups, formation groups, lattice, algebraic lattice, lattice of formations.
@article{DM_2022_34_1_a2,
author = {S. P. Maksakov and M. M. Sorokina},
title = {On algebraicity of lattices of $\omega$-fibred formations of finite groups},
journal = {Diskretnaya Matematika},
pages = {23--35},
publisher = {mathdoc},
volume = {34},
number = {1},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_2022_34_1_a2/}
}
S. P. Maksakov; M. M. Sorokina. On algebraicity of lattices of $\omega$-fibred formations of finite groups. Diskretnaya Matematika, Tome 34 (2022) no. 1, pp. 23-35. http://geodesic.mathdoc.fr/item/DM_2022_34_1_a2/