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On modularity and algebraicity of the lattice of multiply $\omega$-composition Fitting classes
N. Yanga, N. N. Vorob'evb, I. I. Staselkab
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.
Received: 16.07.2022
Revised: 16.07.2022
Accepted: 21.12.2022
Citation:
N. Yang, N. N. Vorob'ev, I. I. Staselka, “On modularity and algebraicity of the lattice of multiply $\omega$-composition Fitting classes”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 4, 76–88
Linking options:
https://www.mathnet.ru/eng/ivm9871 https://www.mathnet.ru/eng/ivm/y2023/i4/p76
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| Abstract page: | 111 | | Full-text PDF : | 24 | | References: | 38 | | First page: | 8 |
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Citation in format AMSBIB
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