University of Isfahan International Journal of Group Theory 2251-7650 4 2 2015 06 01 On soluble groups whose subnormal subgroups are inert 17 24 9373 10.22108/ijgt.2015.9373 EN Ulderico Dardano Dipartimento Matematica e Appl., v. Cintia, M.S.Angelo 5a, I-80126 Napoli (Italy) Silvana Rinauro Dipartimento di Matematica, Informatica ed Economia, Universita della Basilicata, Viale dell'Ateneo Lucano 10, I-85100 Journal Article 2015 03 13 A subgroup H of a group G is called inert if‎, ‎for each $g\in G$‎, ‎the index of $H\cap H^g$ 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. https://ijgt.ui.ac.ir/article_9373_1b5f405a32618ca02d6d467026ade139.pdf