‎we pursue further our‎ ‎investigation‎, ‎begun in [h.~smith‎, ‎groups with all subgroups subnormal or‎ ‎nilpotent-by-{c}hernikov‎, ‎emph{rend‎. ‎sem‎. ‎mat‎. ‎univ‎. ‎padova}‎ ‎126 (2011)‎, ‎245--253] and continued in [g.~cutolo and h.~smith‎, ‎locally finite groups with all subgroups‎ ‎subnormal or nilpotent-by-{c}hernikov‎. ‎emph{centr‎. ‎eur‎. ‎j‎. ‎math.} (to appear)] ‎‎‎of groups $g$ in w...

Subnormal subgroups possessing connected transversals are briefly discussed.

a subgroup h of a group g is called inert if‎, ‎for each $gin g$‎, ‎the index of $hcap h^g$ in $h$ is finite‎. ‎we give a classification ‎of soluble-by-finite groups $g$ in which subnormal subgroups are inert in the cases where $g$ has no nontrivial torsion normal subgroups or $g$‎ ‎is finitely generated‎.