Large soluble groups and the control of embedding properties

Ricerche di Matematica

Volumn 63, Issue 1, 2014, Pages 117-130

  De Falco, M ^a   de Giovanni, F ^a   Musella, C ^a  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

Control of an embedding property; Group of infinite rank

Indexed keywords

EID: 84939890503     PISSN: 00355038     EISSN: 18273491     Source Type: Journal    
DOI: 10.1007/s11587-014-0204-x     Document Type: Article

References (50)

1. Baer, R.: Abzählbar erkennbare gruppentheoretische Eigenshaften. Math. Z. 79, 344–363 (1962)
2. Baer, R., Heineken, H.: Radical groups of finite abelian subgroup rank. Ill. J. Math. 16, 533–580 (1972)
3. Buckley, J., Lennox, J.C., Neumann, B.H., Smith, H., Wiegold, J.: Groups with all subgroups normal-by finite. J. Austr. Math. Soc. Ser. A 59, 384–398 (1995)
4. Casolo, C.: Groups with finite conjugacy classes of subnormal subgroups. Rend. Sem. Mat. Univ. Padova 81, 107–149 (1989)
5. Černikov, N.S.: A theorem on groups of finite special rank. Ukr. Math. J. 42, 855–861 (1990)
6. Černikov, S.N.: On special p-groups. Mat. Sb. 27, 185–200 (1950)
7. Černikov, S.N.: Groups with given properties of classes of infinite subgroups. Ukr. Math. J. 19, 715–731 (1967)
8. De Falco, M., de Giovanni, F., Musella, C.: Groups whose proper subgroups of infinite rank have a transitive normality relation. Mediter. J. Math. 10, 1999–2006 (2013)
9. De Falco, M., de Giovanni, F., Musella, C.: Groups with finitely many conjugacy classes of non-normal subgroups of infinite rank. Colloq. Math. 131, 233–239 (2013)
10. De Falco, M., de Giovanni, F., Musella, C.: Metahamiltonian groups and related topics. Int. J. Group Theory 2(1), 117–129 (2013)
11. De Falco, M., de Giovanni, F., Musella, C.: Groups with normality conditions for subgroups of infinite rank. Publ. Mat. 58, 331–340 (2014)
12. De Falco, M., de Giovanni, F., Musella, C.: A note on soluble groups with the minimal condition on normal subgroups. J. Algebra Appl. 13 (2014) (to appear). doi:10.1142/S021949881350134X
13. De Falco, M., de Giovanni, F., Musella, C.: A note on groups of infinite rank with modular subgroup lattice. Monatsh. Math. (to appear). doi:10.1007/s00605-014-0610-x
14. De Falco, M., de Giovanni, F., Musella, C.: Groups of infinite rank whose subgroups are closed in the profinite topology (to appear)
15. De Falco, M., de Giovanni, F., Musella, C., Sysak, Y.P.: On metahamiltonian groups of infinite rank. J. Algebra 407, 135–148 (2014)
16. De Falco, M., de Giovanni, F., Musella, C., Sysak, Y.P.: Groups of infinite rank in which normality is a transitive relation. Glasgow Math. J. 56, 387–393 (2014)
17. De Falco, M., de Giovanni, F., Musella, C., Trabelsi, N.: Groups with restrictions on subgroups of infinite rank. Rev. Math. Iberoam. 30, 535–548 (2014)
18. De Falco, M., de Giovanni, F., Musella, C., Trabelsi, N.: Groups whose proper subgroups of infinite rank have finite conjugacy classes. Bull. Austr. Math. Soc. 89, 41–48 (2014)
19. De Falco, M., de Giovanni, F., Musella, C., Trabelsi, N.: Groups of infinite rank with finite conjugacy classes of subnormal subgroups (to appear)
20. 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)
21. Dixon, M.R., Evans, M.J., Smith, H.: Some countably recognizable classes of groups. J. Group Theory 10, 641–653 (2007)
22. Dixon, M.R., Karatas, Z.Y.: Groups with all subgroups permutable or of finite rank. Central Eur. J. Math. 10, 950–957 (2012)
23. Eremin, I.I.: Groups with finite classes of conjugate abelian subgroups. Mat. Sb. 47, 45–54 (1959)
24. Evans, M.J., Kim, Y.: On groups in which every subgroup of infinite rank is subnormal of bounded defect. Commun. Algebra 32, 2547–2557 (2004)
25. Franciosi, S., de Giovanni, F., Newell, M.L.: Groups whose subnormal subgroups are normal-by-finite. Commun. Algebra 23, 5483–5497 (1995)
26. Gaschütz, W.: Gruppen in denen das Normalteilersein transitiv ist. J. Reine Angew. Math. 198, 87–102 (1957)
27. de Giovanni, F, Martusciello, M., Rainone, C.: Locally finite groups whose subgroups have finite normal oscillation. Bull. Austr. Math. Soc. 89, 479–487 (2014)
28. Heineken, H., Mohamed, I.J.: A group with trivial centre satisfying the normalizer condition. J. Algebra 10, 368–376 (1968)
29. Kurdachenko, L.A., Smith, H.: Groups in which all subgroups of infinite rank are subnormal. Glasgow Math. J. 46, 83–89 (2004)
30. Kurdachenko, L.A., Smith, H.: Groups with rank restrictions on non-subnormal subgroups. Turk. J. Math. 28, 165–176 (2004)
31. Kuzennyi, N.F., Semko, N.N.: Structure of solvable nonnilpotent metahamiltonian groups. Math. Notes 34, 572–577 (1983)
32. Mal’cev, A.I.: On certain classes of infinite soluble groups. Dokl. Akad. Nauk. SSSR 28, 567–588 (1951)
33. Menth, M.: Nilpotent groups with every quotient residually finite. J. Group Theory 5, 199–217 (2002)
34. Möhres, W.: Auflösbarkeit von Gruppen, deren Untergruppen alle subnormal sind. Arch. Math. (Basel) 54, 232–235 (1990)
35. Neumann, B.H.: Groups with finite classes of conjugate subgroups. Math. Z. 63, 76–96 (1955)
36. Robinson, D.J.S.: Groups in which normality is a transtive relation. Proc. Camb. Philos. Soc. 68, 21–38 (1964)
37. Robinson, D.J.S.: Finiteness Conditions and Generalized Soluble Groups. Springer, Berlin (1972)
38. Robinson, D.J.S., Russo, A., Vincenzi, G.: On groups whose subgroups are closed in the profinite topology. J. Pure Appl. Algebra 213, 421–429 (2009)
39. Romalis, G.M., Sesekin, N.F.: Metahamiltonian groups. Ural. Gos. Univ. Mat. Zap. 5, 101–106 (1966)
40. Romalis, G.M., Sesekin, N.F.: Metahamiltonian groups II. Ural. Gos. Univ. Mat. Zap. 6, 52–58 (1968)
41. Romalis, G.M., Sesekin, N.F.: Metahamiltonian groups III. Ural. Gos. Univ. Mat. Zap. 7, 195–199 (1969)
42. Roseblade, J.E.: On groups in which every subgroup is subnormal. J. Algebra 2, 402–412 (1965)
43. Schmidt, R.: Subgroup Lattices of Groups. de Gruyter, Berlin (1994)
44. Semko, N.N., Kuchmenko, S.N.: Groups with almost normal subgroups of infinite rank. Ukr. Math. J. 57, 621–639 (2005)
45. Smirnov, D.M.: On the theory of finitely approximable groups. Ukr. Mat. Ž. 15, 453–457 (1963)
46. Smith, H., Wiegold, J.: Locally graded groups with all subgroups normal-by-finite. J. Austr. Math. Soc. Ser. A 60, 222–227 (1996)
47. Stonehewer, S.E.: Modular subgroup structure in infinite groups. Proc. Lond. Math. Soc. 32, 63–100 (1976)
48. Šunkov, V.P.: On locally finite groups of finite rank. Algebra Logic 10, 127–142 (1971)
49. Tomkinson, M.J.: On theorems of B.H. Neumann concerning $$FC$$FC-groups. Rocky Mt. J. Math. 11, 47–58 (1981)
50. Zacher, G.: Una relazione di normalità sul reticolo dei sottogruppi di un gruppo. Ann. Mat. Pura Appl. 131, 57–73 (1982)