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Sibirsk. Mat. Zh., 2007, Volume 48, Number 1, Pages 185–191 (Mi smj15)  

This article is cited in 6 scientific papers (total in 6 papers)

Characterization of the soluble one-generated totally saturated formations of finite groups

V. G. Safonov

Francisk Skorina Gomel State University

Abstract: We prove that the finite length condition for the lattice of $\tau$-closed totally saturated subformations of a $\tau$-closed totally saturated formation is equivalent to the finite length condition for this lattice, and it is also equivalent for the formation to be soluble and one-generated.

Keywords: formation of finite groups, totally saturated formation, lattice of formations, $\tau$-closed formation, one-generated formation.

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English version:
Siberian Mathematical Journal, 2007, 48:1, 150–155

Bibliographic databases:

UDC: 512.542
Received: 30.11.2005

Citation: V. G. Safonov, “Characterization of the soluble one-generated totally saturated formations of finite groups”, Sibirsk. Mat. Zh., 48:1 (2007), 185–191; Siberian Math. J., 48:1 (2007), 150–155

Citation in format AMSBIB
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\paper Characterization of the soluble one-generated totally saturated formations of finite groups
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\vol 48
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\pages 185--191
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\pages 150--155
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. G. Safonov, “The property of being algebraic for the lattice of all $\tau$-closed totally saturated formations”, Algebra and Logic, 45:5 (2006), 353–356  mathnet  crossref  mathscinet  zmath
    2. V. G. Safonov, “O suschestvovanii minimalnykh $\tau$-zamknutykh totalno nasyschennykh ne $\mathfrak H$-formatsii”, Tr. In-ta matem., 16:1 (2008), 67–72  mathnet
    3. V. G. Safonov, A. N. Skiba, “O $\tau$-zamknutykh totalno nasyschennykh formatsiyakh $l_\infty^\tau$-dliny $\le 5$”, Tr. In-ta matem., 16:1 (2008), 73–80  mathnet
    4. V. G. Safonov, “$\mathfrak G$-separability of the lattice of $\tau$-closed totally saturated formations”, Algebra and Logic, 49:5 (2010), 470–479  mathnet  crossref  mathscinet  zmath  isi
    5. P. A. Zhiznevskii, “Elementy vysoty 3 reshetki $\tau$-zamknutykh $n$-kratno $\omega$-kompozitsionnykh formatsii”, PFMT, 2011, no. 3(8), 61–68  mathnet
    6. V. G. Safonov, I. N. Safonova, “Otdelimost reshetki $\tau$-zamknutykh totalno $\omega$-nasyschennykh formatsii konechnykh grupp”, PFMT, 2017, no. 4(33), 76–83  mathnet
  • Сибирский математический журнал Siberian Mathematical Journal
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