On the theory of generalized FC-groups

PRONORMALITY IN GENERALIZED FC-GROUPS

“…The proof of this property makes use of the fact that if G is an FC-group, the factor G/Z (G) is periodic. Even if this property is no longer true for FC n -groups (examples can be found in [15]), we will extend the above result as follows. THEOREM 2.1.…”

“…It is easy to check that if the nth term of the upper central series of a group G has finite index in G then G is an FC n -group, in particular every finite-by-nilpotent group is an FC * -group. It is shown in [15] that several theorems concerning the strong form of residual finiteness for FC-groups can be extended to FC * -groups.…”

On Generalised Fc-Groups in Which Normality Is a transitive Relation

“…It can be seen that many of the properties common to finite and nilpotent groups also hold for FC * -groups. The theory of FC *groups has been developed since their first appearance in [4] (see [8,18,19,21]). Some characterisations of soluble FC * -groups in which normality is a transitive relation have been recently obtained (see [11,Theorem 5.2]); moreover, a weak form of transitivity of normality has been recently studied in the universe of all FC * -groups (see [20,Theorem 4.2]).…”

The Engel elements in generalized FC-groups

“…The investigation of properties, that are common to finite groups and nilpotent groups, has been satisfactory for F C * -groups [5,12,13,9]. It turns out that every finite-by-nilpotent group is an F C * -group and, conversely, every F C * -group is locally (finite-by-nilpotent) [5,Proposition 3.6].…”

“…every subgroup of G is an intersection of subgroups of finite index. A complete classification of ERFgroups in the class of F C * -groups is given in [12].…”