On the Brouwer lattices of $\omega$-fibered formations of finite groups

S. P. Maksakov ; M. M. Sorokina

Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2024), pp. 5-17

Résumé

Only finite groups and classes of finite groups are considered. A class of groups is a set of groups that, with each group $G$, contains all groups isomorphic to $G$. In this paper we study formations, i.e. classes of groups that are closed under homomorphic images and subdirect products. The purpose of this paper is to research the lattice properties of $\omega$-fibered formations where $\omega$ is a non-empty set of primes. Sufficient conditions, under which the Brouwer lattice $\omega \delta F (\frak F)$ of all $\omega$-fibered subformations with an arbitrary direction $\delta$ of a given formation $\frak F$ is a Stone lattice, are established. As corollaries of the main theorem, results for $\omega$-local, local formations and other types of formations imply.

Détail

Keywords: finite group, class of groups, $\omega$-fibered formation, lattice, Brouwer lattice, Stone lattice.
Mots-clés : formation

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