Geodesic
On modularity and algebraicity of the lattice of multiply $\omega$-composition Fitting classes
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2023), pp. 76-88

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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. 
@article{IVM_2023_4_a6,
     author = {N. Yang and N. N. Vorob'ev and I. I. Staselka},
     title = {On modularity and algebraicity of the lattice of multiply $\omega$-composition {Fitting} classes},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {76--88},
     publisher = {mathdoc},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_4_a6/}
}
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N. Yang; N. N. Vorob'ev; I. I. Staselka. On modularity and algebraicity of the lattice of multiply $\omega$-composition Fitting classes. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2023), pp. 76-88. http://geodesic.mathdoc.fr/item/IVM_2023_4_a6/