ON SOLUBLE GROUPS WHOSE SUBNORMAL SUBGROUPS ARE INERT.

A subgroup H of a group G is called inert if, for each g ∈ G, the index of H ∩ Hg 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. [ABSTRACT FROM AUTHOR]