Geodesic
Modularity of the lattice of Baer $n$-multiply $\sigma$-local formations
Algebra i logika, Tome 62 (2023) no. 4, pp. 458-478

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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, generalized formation $\sigma$-function, Baer $\sigma$-local formation, Baer $n$-multiply $\sigma$-local formation, complete lattice of formations, modular lattice, algebraic lattice.
Mots-clés : formation 
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     author = {N. N. Vorob'ev},
     title = {Modularity of the lattice of {Baer} $n$-multiply $\sigma$-local formations},
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     publisher = {mathdoc},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2023_62_4_a1/}
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N. N. Vorob'ev. Modularity of the lattice of Baer $n$-multiply $\sigma$-local formations. Algebra i logika, Tome 62 (2023) no. 4, pp. 458-478. http://geodesic.mathdoc.fr/item/AL_2023_62_4_a1/