Algebra and Discrete Mathematics, 2009, № 4 http://dspace.nbuv.gov.ua:80/handle/123456789/150360 2026-04-19T08:13:05Z 2026-04-19T08:13:05Z Groups with many self-normalizing subgroups M. De Falco F. de Giovanni Musella, C. http://dspace.nbuv.gov.ua:80/handle/123456789/157021 2019-06-19T22:27:47Z 2009-01-01T00:00:00Z 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 Groups with many generalized FC-subgroup Russo, A. Vincenzi, G. http://dspace.nbuv.gov.ua:80/handle/123456789/154643 2019-06-15T22:31:06Z 2009-01-01T00:00:00Z 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 The structure of infinite dimensional linear groups satisfying certain finiteness conditions Jose M. Munoz-Escolano Javier Otal Semko, N.N. http://dspace.nbuv.gov.ua:80/handle/123456789/154635 2019-06-15T22:31:34Z 2009-01-01T00:00:00Z 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 Groups with small cocentralizers Javier Otal Semko, N.N. http://dspace.nbuv.gov.ua:80/handle/123456789/154633 2019-06-15T22:31:48Z 2009-01-01T00:00:00Z Groups with small cocentralizers Javier Otal; Semko, N.N. Let G be a group. If S⊆G is a G-invariant subset of G, the factor-group G/CG(S) is called the cocentralizer of S in G. In this survey-paper we review some results dealing with the influence of several cocentralizers on the structure of the group, a direction of research to which Leonid A. Kurdachenko was an active contributor, as well as many mathematicians all around the world. 2009-01-01T00:00:00Z