On soluble groups whose subnormal subgroups are inert

Abstract

A subgroup H of a group G is called inert if‎, ‎for each g∈G ‎, ‎the index of H∩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.

Keywords

• commensurable
• strongly inert
• finitely generated
• HNN-extension