A note on groups with many locally supersoluble subgroups
عنوان مقاله: A note on groups with many locally supersoluble subgroups
شناسه ملی مقاله: JR_THEGR-4-2_002
منتشر شده در در سال 1394
شناسه ملی مقاله: JR_THEGR-4-2_002
منتشر شده در در سال 1394
مشخصات نویسندگان مقاله:
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
خلاصه مقاله:
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
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.
کلمات کلیدی: locally supersoluble group, minimal condition, conjugacy class
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1199973/