Large Characteristic Subgroups with Restricted Conjugacy Classes

Results in Mathematics

Volumn 74, Issue 4, 2019, Pages

  de Giovanni, Francesco ^a   Trombetti, Marco ^a  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

Characteristic subgroup; FC group; metahamiltonian group

Indexed keywords

EID: 85071625599     PISSN: 14226383     EISSN: 14209012     Source Type: Journal    
DOI: 10.1007/s00025-019-1089-5     Document Type: Article

References (27)

1. Bruno, B., Napolitani, F.: A note on nilpotent-by-Černikov groups. Glasg. Math. J. 46, 211–215 (2004)
2. Buckley, J.T., Lennox, J.C., Neumann, B.H., Smith, H., Wiegold, J.: Groups with all subgroups normal-by-finite. J. Aust. Math. Soc. Ser. A 59, 384–398 (1995)
3. Catino, F., de Giovanni, F.: Some Topics in the Theory of Groups with Finite Conjugacy Classes. Aracne, Rome (2015)
4. De Mari, F., de Giovanni, F.: Groups with few normalizer subgroups. Ir. Math. Soc. Bull. 56, 103–113 (2005)
5. de Giovanni, F., Trombetti, M.: Groups with restrictions on proper uncountable subgroups. Stud. Sci. Math. Hung. 56, 154–165 (2019)
6. de Giovanni, F., Trombetti, M.: A note on large characteristic subgroups. Commun. Algebra 46, 4654–4662 (2018)
7. de Giovanni, F., Trombetti, M.: Large characteristic subgroups with modular subgroup lattice. Arch. Math. (Basel) 111, 123–128 (2018)
8. de Giovanni, F., Trombetti, M.: Large characteristic subgroups in which normality is a transitive relation. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 30(29), 255–268 (2019)
9. de Giovanni, F., Trombetti, M.: Large characteristic subgroups and abstract group classes. Quaest. Math. 10.2989/16073606.2019.1602087 (to appear)
10. Franciosi, S., de Giovanni, F., Tomkinson, M.J.: Groups with polycyclic-by-finite conjugacy classes. Boll. Un. Mat. Ital. 4(B), 35–55 (1990)
11. Kargapolov, M.I., Merzljakov, J.I.: Fundamentals of the Theory of Groups. Springer, Berlin (1979)
12. Khukhro, E.I., Makarenko, N.Y.: Large characteristic subgroups satisfying multilinear commutator identities. J. Lond. Math. Soc. 75, 635–646 (2007)
13. Klyachko, A.A., Mel’nikova, Y.B.: A short proof of the Khukhro–Makarenko theorem on large characteristic subgroups with laws. Sb. Math. 200, 661–664 (2009)
14. Klyachko, A.A., Milentyeva, M.: Large and symmetric: the Khukhro–Makarenko theorem on laws—without laws. J. Algebra 424, 222–241 (2015)
15. Kuzennyi, N.F., Semko, N.N.: The structure of infinite nilpotent periodic meta-Hamiltonian groups. In: The Structure of Groups and Subgroup Characterizations Kiev, 101–111 (1984)
16. Kuzennyi, N.F., Semko, N.N.: On the structure of nonperiodic meta-Hamiltonian groups. Sov. Math. (Iz. VUZ) 30, 42–52 (1986)
17. Neumann, B.H.: Groups with finite classes of conjugate subgroups. Math. Z. 63, 76–96 (1955)
18. Ol’shanskiĭ, A.Y.: On characteristic subgroups of free groups. Usp. Mat. Nauk 27, 179–180 (1974)
19. Passman, D.S.: Group rings satisfying a polynomial identity. J. Algebra 20, 103–117 (1972)
20. Podoski, K., Szegedy, B.: Bounds in groups with finite abelian coverings or with finite derived groups. J. Group Theory 5, 443–452 (2002)
21. Robinson, D.J.S.: On the theory of groups with extremal layers. J. Algebra 14, 182–193 (1970)
22. Robinson, D.J.S.: Finiteness Conditions and Generalized Soluble Groups. Springer, Berlin (1972)
23. Romalis, G.M., Sesekin, N.F.: Metahamiltonian groups. Ural. Gos. Univ. Mat. Zap. 5, 101–106 (1966)
24. Romalis, G.M., Sesekin, N.F.: Metahamiltonian groups II. Ural. Gos. Univ. Mat. Zap. 6, 50–52 (1968)
25. Romalis, G.M., Sesekin, N.F.: Metahamiltonian groups III. Ural. Gos. Univ. Mat. Zap. 7, 195–199 (1969/1970)
26. Smith, H., Wiegold, J.: Locally graded groups with all subgroups normal-by-finite. J. Aust. Math. Soc. Ser. A 60, 222–227 (1996)
27. Tomkinson, M.J.: FC -groups. Pitman, Boston (1984)