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Information × Registration Number 0221U105137, 0115U001667 , R & D reports Title The Research of Algebraic and Topological Structures with Given System of Constraints. popup.stage_title Head Lyman Fedir M., Доктор фізико-математичних наук Registration Date 07-06-2021 Organization Sumy State Pedagogical University named after A. S. Makarenko popup.description2  An expanded and detailed survey of existing findings on the problem of studying groups with restrictions on generalized norms has been made. Structural description of finite 2-groups with non-Dedekind non-metacyclic norm of Abelian non-cyclic subgroups and cyclic center is obtained. It is proved that in the class of locally finite groups, which contains an Abelian non-cyclic subgroup, the norm of decomposable subgroups and the norm of Abelian non-cyclic subgroups coincide or one of these norms contains another. Examples of groups that illustrate the relations between these norms are constructed. A structural description of groups that can be norms of decomposable subgroups of a non-periodic locally solvable group is obtained, provided that such a norm is locally nilpotent and non-Dedekind. The structure of non-periodic locally nilpotent groups, in which the norm of Abelian non-cyclic subgroups is non-Dedekind, is described. It is proved that in this case the norm of Abelian non-cyclic subgroups is contained in the norm of decomposable subgroups of a group. The spectral characteristics of the Fourier-Jacobi differential operator are studied and the estimates of Fourier coefficients of generalized functions of Burling type are refined. The concept of re-star convergence is introduced. An overview of the main metric functions that define the topological structure is made: norm, seminorm, pseudonorma, metric, symmetric, quasi-norm, p-norm, s-norm, F-norm. It is proved that a quasibanach lattice, structurally embedded in a topological linear lattice, is embedded in it topologically. The examples of quasi-lattices, in which convergence in the initial quasinorm follows a conformal star convergence with respect to the convergence with the regulator, are constructed. In the topological linear spaces the concept of a strongly bounded set was introduced. It has been proved that the set M is severely limited if and only if it is limited. On the basis of the method of pseudo-in Product Description popup.authors Drushliak Maryna H. Lukashova Tetiana Dmytrivna Martynenko Оlena V Pohrebnyi Valerii D Strakh Oleksandr Petrovych Khvorostina Yurii V Chkana Yaroslav O popup.nrat_date 2021-06-07 Close