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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2017, Issue 4(33), Pages 76–83 (Mi pfmt539)  

This article is cited in 3 scientific papers (total in 3 papers)

MATHEMATICS

Separability of the lattice of ττ-closed totally ωω-saturated formations of finite groups

V. G. Safonov, I. N. Safonova

Belarusian State University, Minsk
Full-text PDF (396 kB) Citations (3)
References:
Abstract: Let X be a non-empty class of finite groups. A complete lattice θ of formations is said to be X-separable if for every term ν(x1,,xn) of signature {,θ}, θ-formations F1,,Fn and every group AXν(F1,,Fn) exists X-groups A1F1,,AnFn, such that Aν(θformA1,,θformAn). In particular, if X=G is the class of all finite groups then the lattice θ of formations is said to be G-separable or, briefly, separable. It is proved that the lattice lτω of all τ-closed totally ω-saturated formations is G-separable for any subgroup functor τ.
Keywords: formation of finite groups, τ-closed formation, totally ω-saturated formation, lattice of formations, G-separated lattice of formations.
Received: 14.11.2017
Document Type: Article
UDC: 512.542
Language: Russian
Citation: V. G. Safonov, I. N. Safonova, “Separability of the lattice of τ-closed totally ω-saturated formations of finite groups”, PFMT, 2017, no. 4(33), 76–83
Citation in format AMSBIB
\Bibitem{SafSaf17}
\by V.~G.~Safonov, I.~N.~Safonova
\paper Separability of the lattice of $\tau$-closed totally $\omega$-saturated formations of finite groups
\jour PFMT
\yr 2017
\issue 4(33)
\pages 76--83
\mathnet{http://mi.mathnet.ru/pfmt539}
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  • https://www.mathnet.ru/eng/pfmt539
  • https://www.mathnet.ru/eng/pfmt/y2017/i4/p76
  • This publication is cited in the following 3 articles:
    1. I. P. Los, V. G. Safonov, “Otdelimost reshetki τ-zamknutykh totalno ω-kompozitsionnykh formatsii konechnykh grupp”, Tr. In-ta matem., 31:2 (2023), 44–56  mathnet
    2. N. N. Vorob'ev, I. I. Stasel'ko, A. O. Hojagulyyev, “Separated lattices of multiply σ-local formations”, Siberian Math. J., 62:4 (2021), 586–597  mathnet  crossref  crossref  isi  elib
    3. V. V. Shcherbina, “Algebraicity of lattice of τ-closed totally ω-saturated formations of finite groups”, Ufa Math. J., 12:1 (2020), 82–90  mathnet  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Проблемы физики, математики и техники
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    Full-text PDF :65
    References:49
     
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