On some classes of finite σ-soluble PσT-groups
https://doi.org/10.29235/1561-83232023-67-6-460-464
Abstract
Let X be a class of groups. Suppose that with each group G ∈ X we associate some system of its subgroups τ(G). Then τ is said to be a subgroup functor on X if the following conditions are hold: (1) G ∈ τ(G) for each group G ∈ X; (2) for any epimorphism φ: A → B, where A, B ∈ X, and for any groups H ∈ τ(A) and T ∈ τ(B) we have Hφ ∈ τ(B) and Tφ-1 ∈ τ( A). In this paper, were considered some applications of such subgroup functors in the theory of finite groups in which generalized normality for subgroups is transitive.
Supporting agencies: Research was supported by the Ministry of Education of the Republic of Belarus (No. 20211328, 20211778)
About the Authors
I. N. Safonova
Belarusian State University
Belarus
Belarus
Safonova Inna N. – Ph. D. (Physics and Mathematics), Associate Professor.
4, Nezavisimosti Ave., 220030, Minsk
A. N. Skiba
Francisk Skorina Gomel State University
Belarus
Belarus
Skiba Alexander N. – D. Sc. (Physics and Mathematics), Professor.
104, Sovetskaya Str., 246019, Gomel
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