On the modularity of the lattice of Baer-σ-local formations
| Autor: | N. N. Vorob’ev |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series. 59:7-17 |
| ISSN: | 2524-2415 1561-2430 |
| Popis: | Throughout this paper, all groups are finite. A group class closed under taking homomorphic images and finite subdirect products is called a formation. The symbol σ denotes some partition of the set of all primes. V. G. Safonov, I. N. Safonova, A. N. Skiba (Commun. Algebra. 2020. Vol. 48, № 9. P. 4002–4012) defined a generalized formation σ-function. Any function f of the form f : σ È {Ø} → {formations of groups}, where f(Ø) ≠ ∅, is called a generalized formation σ-function. Generally local formations or so-called Baer-σ-local formations are defined by means of generalized formation σ-functions. The set of all such formations partially ordered by set inclusion is a lattice. In this paper it is proved that the lattice of all Baerσ-local formations is algebraic and modular. |
| Databáze: | OpenAIRE |
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