A note on groups whose proper subgroups are quasihamiltonian-by-finite

Ricerche di Matematica

Volumn 66, Issue 2, 2017, Pages 619-627

  de Giovanni, Francesco ^a   Saccomanno, Federica ^a  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

Minimal non X group; Quasihamiltonian group

Indexed keywords

EID: 85034006302     PISSN: 00355038     EISSN: 18273491     Source Type: Journal    
DOI: 10.1007/s11587-017-0323-2     Document Type: Article

References (23)

1. Belyaev, V.V.: Groups of Miller–Moreno type. Sib. Math. J. 19, 356–360 (1978)
2. Bruno, B.: On groups with abelian-by-finite proper subgroups. Boll. Un. Mat. Ital. 3, 797–807 (1984)
3. Bruno, B., Phillips, R.E.: Minimal non- FC groups. Abstr. Am. Math. Soc. 2, 565 (1980)
4. Bruno, B., Phillips, R.E.: A note on groups with nilpotent-by-finite proper subgroups. Arch. Math. (Basel) 65, 369–374 (1995)
5. Bruno, B., Napolitani, F.: A note on nilpotent-by-Černikov groups. Glasgow Math. J. 46, 211–215 (2004)
6. de Giovanni, F., Saccomanno, F.: A note on groups of infinite rank whose proper subgroups are abelian-by-finite. Colloq. Math. 137, 165–170 (2014)
7. de Giovanni, F., Trombetti, M.: Groups with minimax commutator subgroup. Int. J. Group Theory 3(1), 9–16 (2014)
8. de Giovanni, F., Trombetti, M.: Groups of infinite rank with a locally finite term in the lower central series. Beitr. Algebra Geom. 56, 735–741 (2015)
9. de Giovanni, F., Trombetti, M.: Infinite minimal non-hypercyclic groups. J. Algebra Appl. 14, 1550143 (2015). doi:10.1142/S0219498815501431
10. De Falco, M., de Giovanni, F., Musella, C.: Groups whose proper subgroups of infinite rank have a transitive normality relation. Mediterr. J. Math. 10, 1999–2006 (2013)
11. De Falco, M., de Giovanni, F., Musella, C.: Large soluble groups and the control of embedding properties. Ric. Mat. 63(suppl.), 117–130 (2014)
12. De Falco, M., de Giovanni, F., Musella, C., Trabelsi, N.: Groups whose proper subgroups of infinite rank have finite conjugacy classes. Bull. Austral. Math. Soc. 89, 41–48 (2014)
13. Dixon, M.R.: Sylow Theory, Formations and Fitting Classes in Locally Finite Groups. World Scientific, Singapore (1994)
14. Dixon, M.R., Evans, M.J., Smith, H.: Locally (soluble-by-finite) groups with all proper non-nilpotent subgroups of finite rank. J. Pure Appl. Algebra 135, 33–43 (1999)
15. Imperatore, D., Russo, A., Vincenzi, G.: Groups whose proper subgroups are generalized FC -groups. J. Algebra Appl. 10, 1301–1308 (2011)
16. Kargapolov, M.I., Merzljakov, J.I.: Fundamentals of the Theory of Groups. Springer, Berlin (1979)
17. Kleidman, P.B., Wilson, R.A.: A characterization of some locally finite simple groups of Lie type. Arch. Math. (Basel) 48, 10–14 (1987)
18. Longobardi, P., Maj, M., Smith, H.: A note on locally graded groups. Rend. Sem. Mat. Univ. Padova 94, 275–277 (1995)
19. Miller, G.A., Moreno, H.C.: Non-abelian groups in which every subgroup is abelian. Trans. Am. Math. Soc. 4, 398–404 (1903)
20. Obraztsov, V.N.: An imbedding theorem for groups and its corollaries. Math. USSR-Sb. 66, 541–553 (1990)
21. Otal, J., Peña, J.M.: Infinite locally finite groups of type PSL(2, K) or Sz(K) are not minimal under certain conditions. Publ. Mat. 32, 43–47 (1988)
22. Robinson, D.J.S.: Finiteness Conditions and Generalized Soluble Groups. Springer, Berlin (1972)
23. Schmidt, R.: Subgroup Lattices of Groups. de Gruyter, Berlin (1994)