Silvana Franciosi

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.

Groups with a supersoluble triple factorization

In the investigation of factorized groups very often one has to study groups with a triple factorization G=AB=AK=BK, where A and B are subgroups and K is a normal subgroup of G (see, for instance, [2,4, 7, 15, 221). In [3] it was shown that under certain liniteness conditions the triple factorized group G satisfies some nilpotency requirement if A, B, and K satisfy the same nilpotency requirement. In the following, similar statements are proved for some supersolubility conditions.

On locally finite groups factorized by locally nilpotent subgroups

Abstract The structure of a periodic radical group G = AB , factorized by two locally nilpotent subgroups A and B , is investigated. In particular, many theorems already known for finite produts of nilpotent groups are extended to the case of periodic radical groups.

Isomorfismi tra reticoli di sottogruppi normali di gruppi nilpotenti senza torsione

RiassuntoIn questo lavoro sono studiati gli isomorfismi tra reticoli di sottogruppi normali di gruppi nilpotenti senza torsione. Si prova che ogni gruppo iperciclico con la struttura normale di gruppo nilpotente senza torsione è un gruppo nilpotente sanza torsione.SummaryLattice isomorphisms between the normal structures of torsion-free nilpotent groups are studied in this paper. We prove that every hypercyclic group with the normal structure of a torsion-free nilpotent group is a torsion-free nilpotent group.

Groups whose subgroups have small automizers

IfH is a subgroup of a groupG, theautomizer ofH inG is the group of all automorphisms ofH induced by elements of its normalizerNG(H). the subgroupH is said to havesmall automizer ifAutG(H)=Inn(H), i.e. ifNG(H)=HCG(H). This article is devoted to the study of groups for which many subgroups have small automizer.

ON NORMAL SUBGROUPS OF PRODUCTS OF NILPOTENT GROUPS

Let G be a group factorized by finitely many pairwise permutable nilpotent subgroups. The aim of this paper is to find conditions under which at least one of the factors is contained in a proper normal subgroup of G.

Groups with many normal-by-finite subgroups

A subgroup H of a group G is said to be normal-by-finite if the core HG of H in G has finite index in H. In this article groups satisfying the minimal condition on subgroups which are not normal-by-finite and groups with finitely many conjugacy classes of subgroups which are not normal-byfinite are characterized.

Sui gruppi sottomodulari infiniti

Lower-modular infinite groups are considered in this paper. We give a generalization of a theorem of Jones and Ito to locally finite groups and to nilpotent-by-abelian groups; moreover we study periodic subgroups of lower-modular groups.

Groups with restrictions on infinite subnormal subgroups

In this article groups are investigated in which every infinite subnormal subgroup has finitely many conjugates or has finite index in its normal closure.

FC-nilpotent products of hypercentral groups.

It is shown that an FC-nilpotent group G = AB = AK — BK which is the product of two hypercentral subgroups A and B and a nilpotent normal subgroup Kof G is hypercentral. This implies that if the FC-nilpotent group G — AB is the product of a proper nilpotent subgroup A and a proper hypercentral subgroup B then A or B is contained in a proper normal subgroup of G. 1991 Mathematics Subject Classification: 20F16.