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Information × Registration Number 0214U002321, 0111U001133 , R & D reports Title Investigation of the structure of groups with restrictions on systems of subgroups and modules associated with them popup.stage_title Head Kurdachenko Leonid, Доктор фізико-математичних наук Registration Date 29-01-2014 Organization Dniepropetrovsk national university popup.description2 The object of research: the structure of groups with restrictions on important systems of subgroups and the structure of the associated modules with them. The aim of research is investigation of the influence of the system of generalized normal (in particular increasing), permutable, Sylow permutable and generalized pronormal subgroups, satisfying natural restrictions on the structure (generalized soluble) groups, as well as the creation of the theory of DG-modules with large systems of G-invariant D-submodules, the ring of scalars D which is a Dedekind domain. Methods of research - the methods of the theory of generalized soluble groups and modules over group rings. It was fined conditions under which classes pronormal (abnormal) and nearly pronormal (nearly abnormal) subgroups coincide. It was described groups which pronormal subgroups are either normal or abnormal. It was described the structure of locally finite and non-periodic locally generalized radical groups in which every cyclic subgroup is self conjugate-permutable, as well as periodic and non-periodic locally graded groups, in which every subgroups are self conjugate-permutable. It was proved the theorem on the existence of complement and supplement to the hypercentral rezidual, in the case where it is Abelian, on the structure of groups in which kontranormal subgroups has normal complement. It was obtained the generalization of the theorems of I. Schur and R. Baer, and their analogues for modules over group rings. It was proved the theorem on the structure and properties of modules with restrictions on the orbits of elements and subspaces, on the structure of infinite groups witch increasing subgroups are either permutable or pronormal, on the structure of infinite groups with restrictions on the Sylow permutable subgroups. It was received tests on pronormal subgroups, description of the linear groups which every subspace has a core of finite codimension, a description of all finite groups, each pronormal subgroups either normal, or abnormal, tests on pronormality of subgroups, the description of infinite groups, in which each subgroup is near pronormal, a description of generalized solvable groups in which the normal closure of each cyclic subgroup of finite section rank. All results are new and meet the highest international standards in the subject. Scientific results introduce in the tutorial process. Scope: science and education. Product Description popup.authors Пипка Олександр Олександрович Чупордя Василь Анатолійович popup.nrat_date 2020-04-02 Close