N. Yang, N. N. Vorob'ev, I. I. Staselka, “On modularity and algebraicity of the lattice of multiply <nobr>$\omega$</nobr>-composition Fitting classes”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, Number 4,Pages <nobr>76

On modularity and algebraicity of the lattice of multiply $\omega$-composition Fitting classes

N. Yang^a, N. N. Vorob'ev^b, I. I. Staselka^b

^a Jiangnan University, Wuxi, 214122 P. R. China
^b Vitebsk State University named after P.M. Masherov, 33 Moskovsky Ave., Vitebsk, 210038 Belarus

Abstract: In this paper it was found the sufficient conditions for the modularity equality for the collections of $n$-multiply $\omega$-composition Fitting classes $(n > 0)$. It was proved that the lattice of all $n$-multiply $\omega$-composition Fitting classes is algebraic $(n \geqslant 0)$.

Keywords: finite group, Fitting class, $\omega$-composition Fitting class, $\omega$-composition $H$-function of a Fitting class, $n$-multiply $\omega$-composition Fitting class, complete lattice of Fitting classes, modular lattice, algebraic lattice.

UDC: 512.542

Received: 16.07.2022
Revised: 16.07.2022
Accepted: 21.12.2022

DOI: 10.26907/0021-3446-2023-4-76-88