University of Isfahan International Journal of Group Theory 2251-7650 4 2 2015 06 01 A note on groups with many locally supersoluble subgroups 1 7 9144 10.22108/ijgt.2015.9144 EN Francesco De Giovanni Dipartimento di Matematica e Applicazioni - University of Napoli Federico II Marco Trombetti Dipartimento di Matematica e Applicazioni - University of Napoli Federico II Journal Article 2015 03 14 It is proved here that if $G$ is a locally graded group satisfying the minimal condition on subgroups which are not locally supersoluble‎, ‎then $G$ is either locally supersoluble or a Cernikov group‎. ‎The same conclusion holds for locally finite groups satisfying the weak minimal condition on non-(locally supersoluble) subgroups‎. ‎As a consequence‎, ‎it is shown that any infinite locally graded group whose non-(locally supersoluble) subgroups lie into finitely many conjugacy classes must be locally supersoluble. https://ijgt.ui.ac.ir/article_9144_9334581bb870e89c7b3b96752c3d4ee3.pdf