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de Giovanni, Francesco, Trombetti, Marco. (1394). A note on groups with many locally supersoluble subgroups. , 4(2), 1-7. doi: 10.22108/ijgt.2015.9144
Francesco de Giovanni; Marco Trombetti. "A note on groups with many locally supersoluble subgroups". , 4, 2, 1394, 1-7. doi: 10.22108/ijgt.2015.9144
de Giovanni, Francesco, Trombetti, Marco. (1394). 'A note on groups with many locally supersoluble subgroups', , 4(2), pp. 1-7. doi: 10.22108/ijgt.2015.9144
de Giovanni, Francesco, Trombetti, Marco. A note on groups with many locally supersoluble subgroups. , 1394; 4(2): 1-7. doi: 10.22108/ijgt.2015.9144

A note on groups with many locally supersoluble subgroups

International Journal of Group Theory
مقاله 2، دوره 4، شماره 2، شهریور 2015، صفحه 1-7    اصل مقاله (184.71 K)
نوع مقاله: Ischia Group Theory 2014
شناسه دیجیتال (DOI): 10.22108/ijgt.2015.9144
نویسندگان
Francesco de Giovanni* ؛ Marco Trombetti
Dipartimento di Matematica e Applicazioni - University of Napoli Federico II
چکیده
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.
کلیدواژه‌ها
locally supersoluble group؛ minimal condition؛ conjugacy class
مراجع
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S. Franciosi, F. de Giovanni and Y. P. Sysak (1999) Groups with many F C-subgroups J. Algebra 218, 165-182
F. de Giovanni and M. Trombetti Infinite minimal non-hypercyclic groups J. Algebra Appl., to app ear DOI: 10.1142/S0219498815501431
O. H. Kegel and B. A. F. Wehrfritz (1973) Local ly Finite Groups North-Holland Mathematical Library, North-Holland Publishing Co., Amsterdam-London, American Elsevier Publishing Co., Inc., New York 3
P. B. Kleidman and R. A. Wilson (1987) A characterization of some lo cally nite simple groups of Lie typ e Arch. Math. (Basel) 48, 10-14
F. Napolitani and E. Pegoraro (1997) On groups with nilpotent-by- Cernikov proper subgroups Arch. Math. (Basel) 69, 89-94
A. Y. Ol'shanski (1991) Geometry of Defining Relations in Groups Kluwer, Dordrecht
D. J. S. Robinson (1972) Finiteness Conditions and Generalized Soluble Groups Springer, Berlin
B. A. F. Wehrfritz (1973) Infinite Linear Groups Springer-Verlag, New York-Heidelb erg
D. I. Zaicev (1968) Groups satisfying the weak minimal condition Ukrain. Math. J. 20, 408-416
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