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TO THE SPECTRAL THEORY OF DISCRETE HAUSDORFF OPERATORS

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Journal of Mathematical Sciences (United States) 2023年第1期271卷 37-46页

作者： Mirotin, Adolf R. Department of Mathematics and Programming Technologies Francisk Skorina Gomel State University Sovietskaya 104 Gomel 246019 Belarus Regional Mathematical Center Southern Federal University Rostov-on-Don 344090 Russian Federation

We show that under an arithmetic condition the spectrum of a bounded multidimensional discrete Hausdorff operator in the Lebesgue space is an annulus (or a disc) centered at the origin, provided the perturbation matrices commute and are either positive or negative definite. Conditions for a point spectrum of such an operator to be empty are given and its norm is computed. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

关键词： Discrete Hausdorff operator Hausdorff operator Lebesgue space Norm of an operator Spectrum

On a Finite Group Generated by Subnormal Supersoluble Subgroups

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arXiv 2022年

作者： Monakhov, Victor S. Department of Mathematics and Programming Technologies Francisk Skorina Gomel State University Belarus

Supersolubility of a finite group G = 〈A,B〉 with the nilpotent derived subgroup G′ is established under the condition that the subgroups A and B are both subnormal and supersoluble. Copyright © 2022, The Authors...

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On finite groups factorised by submodular subgroups

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arXiv 2023年

作者： Monakhov, Victor S. Sokhor, Irina L. Department of Mathematics and Technologies of Programming Francisk Skorina Gomel State University Belarus

A subgroup H of a finite group G is submodular in G if there is a subgroup chain H = H0 ≤ ... ≤ Hi ≤ Hi+1 ≤ ... ≤ Hn = G such that Hi is a modular subgroup of Hi+1 for every i. We investigate finite factorised groups with submodular primary (cyclic primary) subgroups in factors. We indicate a general approach to the description of finite groups factorised by supersolvable submodular subgroups. Copyright © 2023, The Authors. All rights reserved.

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On groups with modular Schmidt subgroups

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arXiv 2023年

作者： Monakhov, Victor S. Sokhor, Irina L. Department of Mathematics and Technologies of Programming Francisk Skorina Gomel State University Belarus

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Formations of Finite Groups in Polynomial Time: F-residuals and F-subnormality

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arXiv 2022年

作者： Murashka, Viachaslau I. Department of Mathematics and Technologies of Programming Francisk Skorina Gomel State University Gomel Belarus

For a wide family of formations F it is proved that the F-residual of a permutation finite group can be computed in a polynomial time. Moreover, if in the previous case F is hereditary, then an F-subnormality of a sub... 详细信息

关键词： Polynomial approximation

A test for a local formation of finite groups to be a formation of soluble groups with the Shemetkov property

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arXiv 2024年

作者： Murashka, V.I. Department of Mathematics and Technologies of Programming Francisk Skorina Gomel State University Gomel Belarus

L.A. Shemetkov posed a Problem 9.74 in Kourovka Notebook to find all local formations F of finite groups such that every finite minimal non-F-group is either a Schmidt group or a group of prime order. All known solutions to this problem are obtained under the assumption that every minimal non-F-group is soluble. Using the above mentioned solutions we present a polynomial in n time check for a local formation F with bounded π(F) to be a formation of soluble groups with the Shemtkov property where n = max π(F).MSC Codes 20D10, 20F19 Copyright © 2024, The Authors. All rights reserved.

关键词： Polynomials

Constructing regular saturated formations of finite soluble groups

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arXiv 2024年

作者： Murashka, Viachaslau I. Department of Mathematics and Technologies of Programming Francisk Skorina Gomel State University Gomel Belarus

For a formation F of finite groups consider a graph whose vertices are elements of a finite group and two vertices are connected by an edge if and only if they generates non-F-group as elements of a group. A hereditary formation F is called regular if the set of all isolated vertices of the described graph coincides with the intersection of all maximal F-subgroups in every group. The constructive description of saturated regular formations of soluble groups which improves the results of Lucchini and Nemmi is obtained in this paper. In particular, it is showed that saturated regular non-empty formations of soluble groups are just hereditary formations F of soluble groups that contains every group all whose cyclic primary subgroups are K-F-subnormal. Also we prove that the lattice of saturated regular formations of soluble groups is lattice isomorphic to the Steinitz’s *** Codes 20D10, 06B23 Copyright © 2024, The Authors. All rights reserved.

关键词： Graph theory

On the residual of a factorized group with widely supersoluble factors

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arXiv 2020年

作者： Monakhov, Victor S. Trofimuk, Alexander A. Department of Mathematics and Programming Technologies Francisk Skorina Gomel State University Gomel246019 Belarus

Let P be the set of all primes. A subgroup H of a group G is called P-subnormal in G, if either H = G, or there exists a chain of subgroups [formula presented]. A group G is called widely supersoluble, w-supersoluble for short, if every Sylow subgroup of G is P-subnormal in G. A group G = AB with P-subnormal w-supersoluble subgroups A and B is studied. The structure of its w-supersoluble residual is obtained. In particular, it coincides with the nilpotent residual of the A-residual of G. Here A is the formation of all groups with abelian Sylow subgroups. Besides, we obtain new sufficient conditions for the w-supersolubility of such group G. Copyright © 2020, The Authors. All rights reserved.

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On σ-arithmetic graphs of finite groups

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arXiv 2020年

作者： Skiba, Alexander N. Department of Mathematics and Technologies of Programming Francisk Skorina Gomel State University Gomel246019 Belarus

Let G be a finite group and σ a partition of the set of all primes P, that is, σ = {σi | i ∈ I}, where P = Si∈I σi and σi∩σj = ∅ for all i 6= j. If n is an integer, we write σ(n) = {σi | σi∩π(n) 6= ∅} a... 详细信息

Let G be a finite group and σ a partition of the set of all primes P, that is, σ = {σi | i ∈ I}, where P = Si∈I σi and σi∩σj = ∅ for all i 6= j. If n is an integer, we write σ(n) = {σi | σi∩π(n) 6= ∅} and σ(G) = σ(|G|). We say that a chief factor H/K is: π-central in G (π ⊆ P) if H/K and G/CG(H/K) are π-groups;σ-central in G if H/K is σi-central in G for some i;the symbol F{σi}(G) denotes the largest normal {σi}-nilpotent subgroup of G. The group G is said to be: σ-soluble if every chief factor H/K of G is a σi-group for some i = i(H/K);σ-nilpotent if every chief factor of G is σ-central in G;{σi}-nilpotent if every chief factor H/K of G with σ(H/K) ∩ σi 6= ∅ is σ-central in G. The symbol Nσ denotes the class of all σ-nilpotent groups;an Nσ-critical group is a non-σnilpotent group whose all proper subgroups are σ-nilpotent. We call a graph Γ with the set of all vertices V (Γ) = σ(G) (G 6= 1) a σ-arithmetic graph of G, and we associate with G 6= 1 the following three directed σ-arithmetic graphs: (1) the σ-Hawkes graph ΓHσ(G) of G is a σ-arithmetic graph of G in which (σi, σj) ∈ E(ΓHσ(G)) if σj ∈ σ(G/F{σi}(G));(2) the σ-Hall graph ΓσHal(G) of G in which (σi, σj) ∈ E(ΓσHal(G)) if for some Hall σi-subgroup H of G we have σj ∈ σ(NG(H)/HCG(H));(3) the σ-Vasil’ev-Murashko graph ΓNσ(G) of G in which (σi, σj) ∈ E(ΓNσ(G)) if for some Nσ-critical subgroup H of G we have σi ∈ σ(H) and σj ∈ σ(H/F{σi}(H)).MSC Codes 20D10, 20D15, 20D20 Copyright © 2020, The Authors. All rights reserved.

关键词： Classification (of information)