On algebraicity of lattices of $\omega$-fibred formations of finite groups

S. P. Maksakov ; M. M. Sorokina

Diskretnaya Matematika, Tome 34 (2022) no. 1, pp. 23-35

Résumé

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.

Détail

Keywords: finite group, class of groups, formation groups, lattice, algebraic lattice, lattice of formations.