%0 Journal Article
%T A note on groups with many locally supersoluble subgroups
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A de Giovanni, Francesco
%A Trombetti, Marco
%D 2015
%\ 06/01/2015
%V 4
%N 2
%P 1-7
%! A note on groups with many locally supersoluble subgroups
%K locally supersoluble group
%K minimal condition
%K conjugacy class
%R 10.22108/ijgt.2015.9144
%X 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.
%U https://ijgt.ui.ac.ir/article_9144_9334581bb870e89c7b3b96752c3d4ee3.pdf