Groups whose proper subgroups of infinite rank have finite conjugacy classes

Bulletin of the Australian Mathematical Society

Volumn 89, Issue 1, 2014, Pages 41-48

  De Falco, M ^a   De Giovanni, F ^a   Musella, C ^a   Trabelsi, N ^b  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^b FERHAT ABBAS UNIVERSITY   (Algeria)

Author keywords

FC group; finite rank

Indexed keywords

EID: 84893655357     PISSN: 00049727     EISSN: 17551633     Source Type: Journal    
DOI: 10.1017/S0004972713000014     Document Type: Article

References (15)

1. B. Amberg, S. Franciosi and F. de Giovanni, Products of Groups (Clarendon Press, Oxford, 1992).
2. V. V. Belyaev, 'Minimal non-FC-groups', Proc. All Union Symposium on Group Theory (Kiev, 1980), pp. 97-108.
3. V. V. Belyaev and N. F. Sesekin, 'On infinite groups of Miller-Moreno type', Acta Math. Acad. Sci. Hungar. 26 (1975), 369-376.
4. N. S. Černikov, 'A theorem on groups of finite special rank', Ukrainian Math. J. 42 (1990), 855-861.
5. M. De Falco, F. de Giovanni, C. Musella and N. Trabelsi, 'Groups with restrictions on subgroups of infinite rank', Rev. Mat. Iberoamericana, to appear.
6. M. R. Dixon, M. J. Evans and H. Smith, 'Locally soluble-by-finite groups of finite rank', J. Algebra 182 (1996), 756-769.
7. M. R. Dixon, M. J. Evans and H. Smith, 'Locally (soluble-by-finite) groups with all proper nonnilpotent subgroups of finite rank', J. Pure Appl. Algebra 135 (1999), 33-43.
8. M. R. Dixon, M. J. Evans and H. Smith, 'Groups with all proper subgroups (finite rank)-bynilpotent', Arch. Math. (Basel) 72 (1999), 321-327.
9. S. Franciosi, F. de Giovanni and Y. P. Sysak, 'Groups with many FC-subgroups', J. Algebra 218 (1999), 165-182.
10. P. B. Kleidman and R. A. Wilson, 'A characterization of some locally finite simple groups of Lie type', Arch. Math. (Basel) 48 (1987), 10-14.
11. M. Kuzucuoglu and R. E. Phillips, 'Locally finite minimal non-FC-groups', Math. Proc. Cambridge Philos. Soc. 105 (1989), 417-420.
12. J. Otal and J. M. Peña, 'Infinite locally finite groups of type PSL(2,K) or Sz(K) are not minimal under certain conditions', Publ. Mat. 32 (1988), 43-47.
13. D. J. S. Robinson, Finiteness Conditions and Generalized Soluble Groups (Springer, Berlin, 1972).
14. V. P. Šunkov, 'On locally finite groups of finite rank', Algebra Logic 10 (1971), 127-142.
15. M. J. Tomkinson, FC-groups (Pitman, Boston, 1984).