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On groups with a restriction on normal subgroups | ||
| International Journal of Group Theory | ||
| مقاله 2، دوره 7، شماره 1، خرداد 2018، صفحه 1-4 اصل مقاله (162.92 K) | ||
| نوع مقاله: Ischia Group Theory 2016 | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2016.21237 | ||
| نویسنده | ||
| Alessio Russo* | ||
| Seconda Universita di Napoli | ||
| چکیده | ||
| The structure of infinite groups in which every (proper) normal subgroup is the only one of its cardinality is investigated in the universe of groups without infinite simple sections. The corrisponding problem for finite soluble groups was considered by M. Curzio (1958). | ||
| کلیدواژهها | ||
| normal subgroup؛ soluble group؛ isomorphism class | ||
| مراجع | ||
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[1] R. Armstrong, Finite groups in which any two subgroups of the same order are isomorphic, Proc Cambridge Philos. Soc., 54 (1958) 18–27.
[2] M. Curzio, Sugli N-gruppi risolubili, Atti Accad Naz. Lincei Rend. Cl. Sci. Fis. Nat. Mat. Nat., 25 (1958) 447–452.
[3] F. de Giovanni and A. Russo, A note on groups with few isomorphism classes of subgroups, Colloquium Mathe-maticum, 144 (2016) 265–271.
[4] F. de Giovanni and M. Trombetti, Uncountable groups with restrictions on subgroups of large cardinality, J. Algebra, 447 (2016) 383–396.
[5] D. J. S. Robinson, Finiteness Conditions and Generalized Soluble Groups Springer, Berlin, (1972).
[6] S. Shelah, On a problem of Kurosh, Jónsson groups and applications, In Word Problem II - the Oxford Book, North-Holland, Amsterdam, (1972) 373–394. | ||
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