Groups with restrictions on proper uncountable subgroups

Studia Scientiarum Mathematicarum Hungarica

Volumn 56, Issue 2, 2019, Pages 154-165

  De Giovanni, Francesco ^a   Trombetti, Marco ^a  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

Metahamiltonian group; Periodic subgroup; Uncountable group

Indexed keywords

EID: 85071615040     PISSN: 00816906     EISSN: 15882896     Source Type: Journal    
DOI: 10.1556/012.2019.56.2.1427     Document Type: Article

References (20)

1. Baer, R., Abzählbar erkennbare gruppentheoretische Eigenschaften, Math. Z., 79 (1962), 344–363.
2. Casolo, C., Groups with finite conjugacy classes of subnormal subgroups, Rend. Sem. Mat. Univ. Padova, 81 (1989), 107–149.
3. De Falco, M., de Giovanni, F., Musella, C. and Trabelsi, N., Groups with restrictions on subgroups of infinite rank, Rev. Mat. Iberoamericana, 30 (2014), 537–550.
4. De Mari, F. and de Giovanni, F., Groups with few normalizer subgroups, Irish Math. Soc. Bulletin, 56 (2005), 103–113.
5. de Giovanni, F. and Trombetti, M., Groups of infinite rank with a locally finite term in the lower central series, Beitr. Algebra Geom., 56 (2015), 735–741.
6. de Giovanni, F. and Trombetti, M., Uncountable groups with restrictions on subgroups of large cardinality, J. Algebra, 447 (2016), 383–396.
7. de Giovanni, F. and Trombetti, M., Nilpotency in uncountable groups, J. Austral. Math. Soc., 103 (2017), 59–69.
8. de Giovanni, F. and Trombetti, M., Countably recognizable classes of groups with restricted conjugacy classes, International J. Group Theory, 7 (2018), n.1, 5–16.
9. de Giovanni, F. and Trombetti, M., A note on uncountable groups with modular subgroup lattice, Arch. Math. (Basel), 107 (2016), 581–587.
10. de Giovanni, F. and Trombetti, M., Countable recognizability and nilpotency properties of groups, Rend. Circ. Mat. Palermo, 66 (2017), 399–412.
11. Kegel, O. H. and Wehrfritz, B. A. F., Locally Finite Groups, North-Holland, Amsterdam (1973).
12. Newman, M. F. and Wiegold, J., Groups with many nilpotent subgroups, Arch. Math. (Basel), 15 (1964), 241–250.
13. Obraztsov, V. N., An embedding theorem for groups and its corollaries, Math. USSR-Sb., 66 (1990), 541–553.
14. Robinson, D. J. S., Groups in which normality is a transitive relation, Proc. Cambridge Philos. Soc., 60 (1964), 21–38.
15. Robinson, D. J. S., Finiteness Conditions and Generalized Soluble Groups, Springer, Berlin (1972).
16. Romalis, G. M. and Sesekin, N. F., Metahamiltonian groups, Ural. Gos. Univ. Mat. Zap., 5 (1966), 101–106.
17. Romalis, G. M. and Sesekin, N. F., Metahamiltonian groups II, Ural. Gos. Univ. Mat. Zap., 6 (1968), 50–52.
18. Romalis, G. M. and Sesekin, N. F., Metahamiltonian groups III, Ural. Gos. Univ. Mat. Zap., 7 (1969/70), 195–199.
19. Shelah, S., On a problem of Kurosh, Jónsson groups, and applications, in: Word Problems II – the Oxford Book, North-Holland, Amsterdam (1980), 373–394.
20. Smith, H., Groups with few non-nilpotent subgroups, Glasgow Math. J., 39 (1997), 141–151.