On the modularity of a lattice of τ-closed n-multiply ω-composite formations

Vorob’ëv, N. N.; Tsarev, Aleksandr

doi:10.1007/s11253-010-0368-9

Cited by 18 publications

(7 citation statements)

References 6 publications

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“…Remark 2. Corollary 4 generalises Theorem 3.1 in[23], part 6 of Lemma 1 in[27], Corollaries 5-6 in[9], and Corollary 9.9 in[1].…”

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confidence: 52%

The lattices of n-multiply Ω1-foliated τ-closed formations of multioperator T -groups

Demina¹

2012

Discrete Mathematics and Applications

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In this paper, it is shown that the lattice 1 F ' n of all n-multiply 1 -foliated -closed M-formations with direction ', ' 0 ', for any n 2 N 0 is algebraic, modular, and complete in M, where M is the class of all multioperator T -groups satisfying the minimality and maximality conditions for T -subgroups. We give a complete description of n-multiply 1 -foliated -closed M-formations F with l ‚ .F/ 2, where ‚ D 1 F ' n , n 2 N 0 , and ' 0 '. We also investigate n-multiply 1 -foliated -closed M-formations with r-direction ' such that '.A/ M A 0 M A for all A 2 I 1 for which the lattice of all n-multiply 1 -foliated -closed M-formations with direction ' is Boolean.

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“…Remark 2. Corollary 4 generalises Theorem 3.1 in[23], part 6 of Lemma 1 in[27], Corollaries 5-6 in[9], and Corollary 9.9 in[1].…”

supporting

confidence: 52%

The lattices of n-multiply Ω1-foliated τ-closed formations of multioperator T -groups

Demina¹

2012

Discrete Mathematics and Applications

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“…A satellite f is called Θ-valued if all its values belong to Θ (see [23]). Lemmas 2.1 and 3.1 of [28] imply the following result.…”

Section: Preliminariesmentioning

confidence: 72%

On a Question of the Theory of Partially Composition Formations

Tsarev

Vorob’ëv

2014

Algebra Colloq.

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“…The algebraicity of the lattice of all -mutliply composite formations is implied by the algebraicity of the lattice for a trivial subgroup functor and = P, which was obtained earlier in a joint work of N.N. Vorob'ev and A.A. Tsarev [19], see also [8,Ch. 4,Thm.…”

Section: General Remarksmentioning

confidence: 85%

“…The algebraicity of the lattice of all -closedmutliply solubly -saturated formations was proved by N.N. Vorob'ev and A.A. Tsarev [19], see also [8,Ch. 4,Thm.…”

Section: Introductionmentioning

confidence: 99%

Algebraicity of lattice of $\tau$-closed totally $\omega$-saturated formations of finite groups

Щербина

2020

Ufimsk. Mat. Zh.

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All groups considered in this paper are assumed to be finite. The symbol denotes some nonempty set of primes, and is a subgroup functor in the sense of A.N. Skiba. We recall that a formation is a class of groups that is closed under taking homomorphic images and finite subdirect products. Functions of the form : ∪ { ′ } → {formations of groups} are called-local satellites (formation-functions). Such functions are used to study the structure of-saturated formations. The paper is devoted to studying the properties of the lattice of all closed functorially totally partially saturated formations related to the algebraicity concept for a lattice of formations. We prove that for each subgroup functor , the lattice ∞ of all-closed totally-saturated formations is algebraic. This generalizes the results by V.G. Safonov. In particular, we show that the lattice ∞ of all-closed totally-saturated formations is algebraic as well as the lattice ∞ of all-closed totally saturated formations. Similar results are obtained for lattices of functorially closed totally partially saturated formations corresponding to certain subgroup functors. Thus, we find new classes of algebraic lattices of formations of finite groups.

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On the modularity of a lattice of τ-closed n-multiply ω-composite formations

Cited by 18 publications

References 6 publications

The lattices of n-multiply Ω1-foliated τ-closed formations of multioperator T -groups

The lattices of n-multiply Ω1-foliated τ-closed formations of multioperator T -groups

On a Question of the Theory of Partially Composition Formations

Algebraicity of lattice of $\tau$-closed totally $\omega$-saturated formations of finite groups

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