On σ-local classes of finite groups

Proceedings of the National Academy of Sciences of Belarus Physics and Mathematics Series 2026 Open access

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Authors: Vasily G. Safonov, Inna Nikolaevna Safonova
DOI: 10.29235/1561-2430-2025-61-4-271-287
Cited by: 0
References: 22

Abstract

For various partitions of the set P of all prime numbers, properties of generalized local classes (formations, Fitting classes) of finite groups are investigated. Criteria for σ-locality of an α-local class of groups are proved, where σ and α are some distinct partitions of P. Properties of products of generalized local classes, as well as their algebras, are studied. For a σ-soluble σ-local class, sufficient conditions for the commutativity of the σ-algebra generated by it are obtained.

Fields of Study & Subjects

Finite Group Theory Research Rings Modules and Algebras Advanced Algebra and Logic

Publication details

Journal / source
Proceedings of the National Academy of Sciences of Belarus Physics and Mathematics Series
Volume
61
Issue
4
Pages
271–287
Publication date
6 January 2026