http://dspace.nbuv.gov.ua:80/handle/123456789/150356 2026-04-15T02:34:38Z http://dspace.nbuv.gov.ua:80/handle/123456789/157021 Groups with many self-normalizing subgroups M. De Falco; F. de Giovanni; Musella, C. This paper investigates the structure of groups in which all members of a given relevant set of subgroups are selfnormalizing. In particular, soluble groups in which every nonabelian (or every infinite non-abelian) subgroup is self-normalizing are described. 2009-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154643 Groups with many generalized FC-subgroup Russo, A.; Vincenzi, G. Let FC⁰ be the class of all finite groups, and for each non-negative integer n define by induction the group class FCⁿ⁺¹ consisting of all groups G such that the factor group G/CG(xG) has the property FCⁿ for all elements x of G. Clearly, FC¹ is the class of FC-groups and every nilpotent group with class at most m belongs to FCm. The class of FCⁿ-groups was introduced in [6]. In this article the structure of groups with finitely many normalizers of non-FCⁿ-subgroups (respectively, the structure of groups whose subgroups either are subnormal with bounded defect or have the property FCⁿ) is investigated. 2009-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154638 A new characterization of groups with central chief factors Juriaans, O.S.; Raphael, D.M. In [1] it is proved that a locally nilpotent group is an (X)-group arising the question whether the converse holds. In this paper we derive some interesting properties and give a complete characterization of (X)-groups. As a consequence we obtain a new characterization of groups whose chief factors are central and it follows also that there exists an (X)-group which is not locally nilpotent, thus answering the question raised in [1]. We also prove a result which extends one on finitely generated nilpotent groups due to Gruenberg. 2009-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154635 The structure of infinite dimensional linear groups satisfying certain finiteness conditions Jose M. Munoz-Escolano; Javier Otal; Semko, N.N. We review some recent results on the structure of infinite dimensional linear groups satisfying some finiteness conditions on certain families of subgroups. This direction of research is due to Leonid A. Kurdachenko, who developed the main steps of the theory jointly with mathematicians from several countries. 2009-01-01T00:00:00Z