Leonid A. Kurdachenko

Groups with Prescribed Quotient Groups and Associated Module Theory

Simple Modules: On Annihilators of Modules The Structure of Simple Modules Over Abelian Groups The Structure of Simple Modules Over Some Generalization of Abelian Groups Complements of Simple Submodules Just Infinite Modules: Some Results on Modules Over Dedekind Domains Just Infinite Modules Over FC-Hypercentral Groups Just Infinite Modules Over Groups of Finite 0-Rank Just Infinite Modules Over Polycyclic-By-Finite Groups Co-Layer-Finite Modules Over a Dedekind Domains Just Non-X-Groups: The Fitting Subgroup of Some Just Non-X-Groups Just Non-Abelian Groups Just Non-Hypercentral Groups and Just Non-Hypercentral Modules Groups with Many Nilpotent Factor-Groups Groups with Proper Periodic Factor-Groups Just Non-(Polycyclic-By-Finite) Groups Just Non-CC-Groups and Related Classes Groups Whose Proper Factor-Groups Have a Transitive Normality Relation.

Groups with subnormality for all subgroups that are not finitely generated

SummaryWe characterize the groups given in the title in the case of locally finite, locally nilpotent and radical groups.SuntoI gruppi con tutti i sottogruppi nonfinitamente generati subnormali sono caratterizzati nella classe dei gruppi localmente finiti, localmente nilpotenti e radicali.

On groups with many almost normal subgroups

SummaryAn anti-FC-group is a group in which every subgroup either is finitely generated or has only a finite number of coniugates. In this article a classification is given of (generalized) soluble anti-FC-groups which neither are central-by-finite nor satisfy the maximal condition on subgroups. Moreover, groups in which every non-cyclic subgroup has only a finite number of coniugates are characterized.

Linear groups with the maximal condition on subgroups of infinite central dimension

Let A a vector opace over a ficid E and let H be a subgroop of GL(F, A). We define centdimF H tu be dimF(A/CA(H)). Wc say tbat H bas finite central dimeosion if centdimF H is finite and we say tbat H bao inJlnite central dimeosiso otherwise. We consider soluble linear groups, in which the (ordered by inclusion) set of ah subgroups baving infinite central dimension satisfies tbe maximal condition.

Infinite groups with many permutable subgroups

A subgroup H of a group G is said to be permutable in G, if HK = KH for every subgroup K of G. By a result due to Stonehewer, every permutable subgroup is ascendant although the converse is false. On the other hand, permutability is not a transitive relation. In this paper we study some inflnite groups whose ascendant subgroups are permutable. These groups are very close to the groups in which the relation to be a permutable subgroup is transitive. 2001 MSC: Primary: 20F99.

The rank of the factor-group modulo the hypercenter and the rank of the some hypocenter of a group

We compare the special rank of the factors of the upper central series and terms of the lower central series of a group. As a consequence we are able to show some generalizations of a theorem of Reinhold Baer.

GROUPS IN WHICH ALL SUBGROUPS OF INFINITE RANK ARE SUBNORMAL

Let

On some criteria of nilpotency.

G

Abnormal, Pronormal, Contranormal, and Carter Subgroups in Some Generalized Minimax Groups

be a locally soluble-by-finite group in which every non-subnormal subgroup has finite rank. It is proved that either

Pronormality, contranormality and generalized nilpotency in infinite groups

G