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Information × Registration Number 0224U002019, 0118U004755 , R & D reports Title Infinite groups with constraints for subgroups and the implementation of interobject connections in the process of teaching mathematical dispines in economic higher education establishments popup.stage_title Head Semko Nikolaj N., Доктор фізико-математичних наук Registration Date 04-02-2024 Organization State Tax University popup.description2 Report on DiR: 113c., 130 sources. The object of the study is normal subgroups, Chernikov groups, groups with dense systems of normal subgroups, intersubject connections, the process of teaching mathematics to students of higher education institutions. The purpose of the work is the effective application of normality conditions for the study of the structure of infinite groups, the study and generalization of intersubject relationships in the process of teaching mathematical disciplines in economic universities. The research method is modern methods of group theory, modern methods of teaching mathematics in universities and secondary educational institutions. Work results. The work is devoted to the study of generalizations of dedekind groups, which is carried out thanks to different normality density conditions for subgroups. In other words, we study groups G that have a normal subgroup N placed between any two subgroups A and B of group G, where A is a subgroup of B. Different density conditions are determined by the ratios: A N B; A<N<B; A<N B; And N<B, as well as properties: A is a subgroup of group B; A is a proper subgroup of group B; A is a proper non-maximal subgroup of group B. Certain classes of locally graded groups with conditions of different normality densities for subgroups have been studied. The methodology of teaching students to prove theorems has been researched and analyzed, in particular, the methodology of teaching ready-made proofs and teaching students to independently search for proofs, the method of full induction and the method of mathematical induction are given. The results of the work are published in 108 works, of which 18 are indexed in the SCOPUS database. Keywords: Dedekind group, normal subgroup, density of normality, proper subgroup, proper non-maximal subgroup, segment of subgroups, learning system, learning method, proof, analytical-synthetic method, method of mathematical induction. Product Description popup.authors Bilorus Tetiana V. Semko Mykola M. Skaskiv Liliya V. Fedun Inna V. Chernobay Olha B. Yarova Oksana A. popup.nrat_date 2024-02-04 Close