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.
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de Giovanni, F. and Trombetti, M. (2015). A note on groups with many locally supersoluble subgroups. International Journal of Group Theory, 4(2), 1-7. doi: 10.22108/ijgt.2015.9144
MLA
de Giovanni, F. , and Trombetti, M. . "A note on groups with many locally supersoluble subgroups", International Journal of Group Theory, 4, 2, 2015, 1-7. doi: 10.22108/ijgt.2015.9144
HARVARD
de Giovanni, F., Trombetti, M. (2015). 'A note on groups with many locally supersoluble subgroups', International Journal of Group Theory, 4(2), pp. 1-7. doi: 10.22108/ijgt.2015.9144
CHICAGO
F. de Giovanni and M. Trombetti, "A note on groups with many locally supersoluble subgroups," International Journal of Group Theory, 4 2 (2015): 1-7, doi: 10.22108/ijgt.2015.9144
VANCOUVER
de Giovanni, F., Trombetti, M. A note on groups with many locally supersoluble subgroups. International Journal of Group Theory, 2015; 4(2): 1-7. doi: 10.22108/ijgt.2015.9144