On the existence of H 𝜏σ -critical formations of finite groups
https://doi.org/10.29235/1561-2430-2026-62-1-7-14
Abstract
The 𝜏 -closed σ-local formations of finite groups are studied, where σ is some partition of the set of all primes, 𝜏 is an arbitrary subgroup functor. The question of the existence of 𝜏 Hσ -critical formations is investigated, i. e., such 𝜏 -closed σ-local formations L H ⊆ for which all proper 𝜏 -closed σ-local subformations are contained in the class of groups H. It is proved that if H is a σ-local formation of classical type, then every 𝜏 -closed σ-local formation F H ⊆ has at least one H𝜏 σ - critical subformation.
Keywords
finite group,
subgroup functor,
τ-closed formation,
formation σ-function,
σ-local formation,
critical σ-local formation,
formation of classical type
Supporting agencies: The research was carried out in the framework of the State Program of Scientific Research “Convergence – 2025” with financial support of the Ministry of Education of the Republic of Belarus (project 20211328).
About the Authors
V. V. Skrundz
Belarusian State University
Belarus
Belarus
Valentina V. Skrundz – Postgraduate Student of the Department of Higher Algebra and Information Security
Nezavisimosti Ave., 4, 220030, Minsk
I. N. Safonova
Belarusian State University
Belarus
Belarus
Inna N. Safonova – Dr. Sc. (Physics and Mathematics), Associate Professor, Professor of the Department of Higher Algebra and Information Security
Nezavisimosti Ave., 4, 220030, Minsk
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