On groups with a restriction on normal subgroups

Document Type: Ischia Group Theory 2016


Seconda Universita di Napoli


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)‎.


Main Subjects

[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.