𝜔-fibered Formations of Finite Groups
https://doi.org/10.22405/2226-8383-2021-22-3-232-244
Abstract
Only finite groups are considered. The work is devoted to the study of formations which are classes of groups that are closed with respect to homomorphic images and subdirect products.
For a non-empty set 𝜔 of primes V.A. Vedernikov, using two types of functions, defined 𝜔-fibered formations of finite groups. Developing this functional approach, in the paper for an arbitrary
partition ¯𝜔 of the set 𝜔 we constructed ¯𝜔-fibered formations. The construction uses the 𝜎- concept of A.N. Skiba for the study of finite groups and their classes, where 𝜎 is an arbitrary partition of the set P of all primes. We gave examples of ¯𝜔-fibered formations, established their properties (existence of ¯𝜔-satellites of different types; sufficient conditions for a group 𝐺 to belong to an ¯𝜔-fibered formation; relationship with 𝜔-fibered and P𝜎-fibered formations).
About the Authors
Marina Mikhailovna Sorokina
Bryansk State University named after I. G. Petrovsky
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
Anastasia Andreevna Gorepekina
Bryansk State University named
after I. G. Petrovsky
Russian Federation
Russian Federation
postgraduate student
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Review
For citations:
Sorokina M.M., Gorepekina A.A. 𝜔-fibered Formations of Finite Groups. Chebyshevskii Sbornik. 2021;22(3):232-244. (In Russ.) https://doi.org/10.22405/2226-8383-2021-22-3-232-244
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