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Information × Registration Number 0215U001885, 0111U005735 , R & D reports Title The investigation of difficult algebraic and topological structures. popup.stage_title Head Lyman Fedir Mycolayovych, Доктор фізико-математичних наук Registration Date 24-06-2015 Organization Sumy State Pedagogical University named by Makarenko popup.description2 The object: mathematical structures with limitations of algebraic and topological types. The subject: groups, spaces of abstract convergence, divergent sequences, series, classes of functions, differential equations and random variables. Purpose: - research of the structural properties of different classes of groups depending on the properties of their generalized norms; - identification the connections between different generalized norms and research of their influence to the structure of the group; construction the examples of relevant groups; - research of the properties of groups with the condition of Separator normality for various systems of subgroups and linkages with already known classes; - construction of structures of double star convergence and research of connections at different ways of formation of such structures; - comparative analysis of passive and adaptive coding methods of different classes of curves and surfaces; - setting limit values for functions from the domain of the maximal operator of Jacobi; - working out the methods of summation the divergent numerical series; - research of random variables, represented by the alternating rows of Luroth; - characterization the conditions of existence of solutions of integro-dynamical system with degenerate kernel on the timeline and Noetherian boundary value problem for it; in the case of solvability to construct the general solution. For realization the goals there were used the classical methods of general algebra, group theory, the theory of images, classic and metric number theory, mathematical, functional and fractal analysis, the theory of functions of the real variable, differential equations, measure theory and probability theory. During the reporting period the authors of the project revealed new approaches and worked out some new methods in the following issues: - characterization of groups where restrictions concern the norms and separators of given systems of subgroups; - research of the іmpact of double star convergences in connection with the axioms of the class convergence by A. Word; - finding estimates of extreme characteristics of the classes of curves and surfaces in different metrics and comparative analysis of passive and adaptive methods of their coding; - summation of the divergent series by matrix methods; - research of the characteristic function of random variable presented by random subsumes of alternating series by Luroth, the terms of which form a homogeneous Markov's chain; - research of the solvability conditions of integral-dynamic systems with degenerate kernel on the timeline. The results of the research are the following: 1) set up the comprehensive characterization of the finite p-groups with non-Dedekind norm of Abelian noncyclic subgroups (provided that such a rule differs from the Dihedral group); the structural description of locally finite groups with a locally nilpotent norm of Abelian noncyclic subgroups was obtained; 2) proved that in the class of finite p-group norms of noncyclic Abelian subgroups and norms of decomposable subgroups are the same. In the class of finite nonprime groups, where the set of Abelian noncyclic subgroups is not empty, the norm of noncyclic Abelian subgroups contains the norm of decomposable subgroups, moreover, the inclusion may be strict; 3) found out that in a class of infinite periodic locally nilpotent groups the norm of the decomposable subgroups also contained in the norm of Abelian noncyclic subgroups, provided that the system of noncyclic Abelian subgroups of the group is nonempty; 4) proved that in a group G with separating system of subgroups , which consists of either all, or cyclic, or noncyclic, or Abelian or non-Abelian, or nilpotent, or non-nilpotent, or infinite subgroups of the group G, the following statement have place: - the arbitrary non-single Н( )-group G is a group with a single separator$ - if U is a sub-group of Н( Product Description popup.authors Власенко В. Ф. Друшляк М.Г. Лиман Ф.М. Лукашова Т.Д. Мартиненко О.В. Одінцова О.О. Погребний В.Д. Страх О.П. Хворостіна Ю.В. Чкана Я.О. popup.nrat_date 2020-04-02 Close