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

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.