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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2017, Issue 4(33), Pages 76–83
(Mi pfmt539)
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This article is cited in 3 scientific papers (total in 3 papers)
MATHEMATICS
Separability of the lattice of ττ-closed totally ωω-saturated formations of finite groups
V. G. Safonov, I. N. Safonova Belarusian State University, Minsk
Abstract:
Let X be a non-empty class of finite groups. A complete lattice θ of formations is said to be X-separable if for every term ν(x1,…,xn) of signature {∩,∨θ}, θ-formations F1,…,Fn and every group A∈X∩ν(F1,…,Fn)
exists X-groups A1∈F1,…,An∈Fn, such that A∈ν(θformA1,…,θformAn). In particular, if X=G is the class of all finite groups then the lattice θ of formations is said to be G-separable or, briefly, separable. It is proved that the lattice lτω∞ of all τ-closed totally ω-saturated formations is G-separable for any subgroup functor τ.
Keywords:
formation of finite groups, τ-closed formation, totally ω-saturated formation, lattice of formations, G-separated lattice of formations.
Received: 14.11.2017
Citation:
V. G. Safonov, I. N. Safonova, “Separability of the lattice of τ-closed totally ω-saturated formations of finite groups”, PFMT, 2017, no. 4(33), 76–83
Linking options:
https://www.mathnet.ru/eng/pfmt539 https://www.mathnet.ru/eng/pfmt/y2017/i4/p76
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Abstract page: | 221 | Full-text PDF : | 65 | References: | 49 |
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