A local study of group classes

It was established in [15] that the class of groups with a finite commutator subgroup can be locally described by locally graded groups having a bound on the length of particular chains of non-normal subgroups. This approximation was later extended to groups having a finite normal subgroup whose factor group has no non-permutable subgroups (see [18]). The aim of this paper is to show that these approximating group classes behave better than the classes they approximate, and can be used to derive new results on these.