Modularity of the lattice of Baer $n$-multiply $\sigma$-local formations

N. N. Vorob'ev

Vitebsk State University named after P. M. Masherov

Abstract: Let $\sigma$ be a partition of the set of all prime numbers into a union of pairwise disjoint subsets. Using the idea of multiple localization due to A. N. Skiba, we introduce the notion of a Baer $n$-multiply $\sigma$-local formation of finite groups. It is proved that with respect to inclusion $\subseteq$, the collection of all such formations form a complete algebraic modular lattice. Thereby we generalize the result obtained by A. N. Skiba and L. A. Shemetkov in [Ukr. Math. J., 52, No. 6, 783–797 (2000)].

Keywords: finite group, formation, generalized formation $\sigma$-function, Baer $\sigma$-local formation, Baer $n$-multiply $\sigma$-local formation, complete lattice of formations, modular lattice, algebraic lattice.

UDC: 512.54.03

Received: 24.01.2023
Revised: 19.07.2024

DOI: 10.33048/alglog.2023.62.402

 English version: Algebra and Logic, 2023, 62:4, 303–318