On Shemetkov’s problem of describing critical formations in the class of τ-closed σ-local formations

Authors

  • Valentina V. Skrundz Belarusian State University, 4 Niezaliezhnasci Avenue, Minsk 220030, Belarus
  • Inna N. Safonova Belarusian State University, 4 Niezaliezhnasci Avenue, Minsk 220030, Belarus

Keywords:

finite group, subgroup functor, τ-closed formation, formation σ-function, σ-local formation, critical σ-local formation, formation of classical type
Supporting Agencies
This research was supported by the Ministry of Education of the Republic of Belarus (grant No. 20211328). The authors thank the referee for careful reading of the paper.

Abstract

The critical τ-closed σ-local formations of finite groups are studied, where σ is some partition of the set of all primes P, τ is an arbitrary subgroup functor. A description of minimal τ-closed σ-local non-H-formations is obtained for an arbitrary σ-local formation of classical type, i. e. a σ-local formation that has a σ-local definition all of whose non-Abelian values are σ-local formations. Thus, the problem of describing critical formations in the class of τ-closed σ-local formations proposed by L. A. Shemetkov (1980) is solved.

Author Biographies

  • Valentina V. Skrundz, Belarusian State University, 4 Niezaliezhnasci Avenue, Minsk 220030, Belarus

    postgraduate student at the department of higher algebra and information security, faculty of mechanics and mathematics

  • Inna N. Safonova, Belarusian State University, 4 Niezaliezhnasci Avenue, Minsk 220030, Belarus

    doctor of science (physics and mathematics), docent; professor at the department of higher algebra and information security, faculty of mechanics and mathematics

References

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Published

2026-06-01

Issue

No. 1 (2026): Journal of the Belarusian State University. Mathematics and Informatics

Section

Mathematical Logic, Algebra and Number Theory

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How to Cite

[1]
Skrundz, V.V. and Safonova, I.N. 2026. On Shemetkov’s problem of describing critical formations in the class of τ-closed σ-local formations. Journal of the Belarusian State University. Mathematics and Informatics. 1 (Jun. 2026), 163–178.