Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-06-11T09:35:18.422Z Has data issue: false hasContentIssue false
  • English
  • Français

PRONORMALITY IN GENERALIZED FC-GROUPS

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  14 September 2010

E. ROMANO  and
G. VINCENZI
E. ROMANO
Affiliation:
Dipartimento di Matematica e Informatica, Università di Salerno, Salerno, Italy (email: eromano@unisa.it)
G. VINCENZI*
Affiliation:
Dipartimento di Matematica e Informatica, Università di Salerno, Salerno, Italy (email: gvincenzi@unisa.it)
*
✉For correspondence; e-mail: gvincenzi@unisa.it
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We extend some results known for FC-groups to the class FC* of generalized FC-groups introduced in de Giovanni et al. [‘Groups with restricted conjugacy classes’, Serdica Math. J.28(3) (2002), 241–254]. The main theorems pertain to the join of pronormal subgroups. The relevant role that the Wielandt subgroup plays in an FC*-group is pointed out.

Keywords

generalized FC-groupspronormalityWielandt subgroup

MSC classification

Secondary: 20E34: General structure theorems 20F19: Generalizations of solvable and nilpotent groups 20F24: FC-groups and their generalizations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 83 , Issue 2 , April 2011 , pp. 220 - 230
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

[1]Ballester-Bolinches, A., Pedraza-Aguilera, M. C. and Pérez-Ramos, M. D., ‘On Π-normally embedded subgroups of finite soluble groups’, Rend. Semin. Mat. Univ. Padova 96 (1996), 115–120.Google Scholar
[2]de Giovanni, F., Russo, A. and Vincenzi, G., ‘Groups with restricted conjugacy classes’, Serdica Math. J. 28(3) (2002), 241–254.Google Scholar
[3]de Giovanni, F. and Vincenzi, G., ‘Groups satisfying the minimal condition on non-pronormal subgroups’, Boll. Unione Mat. Ital. (7) 9A (1995), 185–194.Google Scholar
[4]de Giovanni, F. and Vincenzi, G., ‘Pronormality in infinite groups’, Proc. Roy. Irish Acad. 100A (2000), 189–203.Google Scholar
[5]de Giovanni, F. and Vincenzi, G., ‘Some topics in the theory of pronormal subgroups of groups’, Quad. Mat. 8 (2001), 175–202.Google Scholar
[6]Gaschütz, W., ‘Gruppen, in denen das Normalteilersein transitiv ist’, J. reine angew. Math. 198 (1957), 87–92.CrossRefGoogle Scholar
[7]Herzfeld, U. C., ‘On generalized covering subgroups and a characterisation of pronormal’, Arch. Math. (Basel) 41 (1983), 404–409.CrossRefGoogle Scholar
[8]Kurdachenko, L. A., Otal, J. and Subbotin, I. Y., ‘On properties of abnormal and pronormal subgroups in some infinite groups’, Groups St. Andrews 2005 2 (2007), 597–604.CrossRefGoogle Scholar
[9]Kuzennyi, N. F. and Subbotin, I. Y., ‘Groups with pronormal primary subgroups’, Ukrainian Math. J. 41 (1989), 286–289.CrossRefGoogle Scholar
[10]Legovini, P., ‘Catene pronormali nei gruppi finiti supersolubili’, Rend. Sem. Mat. Univ. Padova 66 (1981), 181–191.Google Scholar
[11]Peng, T. A., ‘Finite groups with pro-normal subgroups’, Proc. Amer. Math. Soc. 20 (1969), 232–234.CrossRefGoogle Scholar
[12]Robinson, D. J. S., ‘Group in which normality is a transitive relation’, Proc. Cambridge Philos. Soc. 60 (1964), 21–38.CrossRefGoogle Scholar
[13]Robinson, D. J. S., ‘A note on finite groups in which normality is transitive’, Proc. Amer. Math. Soc. 19 (1968), 933–937.CrossRefGoogle Scholar
[14]Robinson, D. J. S., Finiteness Condition and Generalized Soluble Groups (Springer, Berlin, 1972).CrossRefGoogle Scholar
[15]Robinson, D. J. S., Russo, A. and Vincenzi, G., ‘On the theory of generalized FC-groups’, J. Algebra (2009), doi:10.1016/j.jalgebra.2009.04.002.Google Scholar
[16]Rose, J. S., ‘Finite soluble groups with pronormal system normalizers’, Proc. London Math. Soc. (3) 17 (1967), 447–469.CrossRefGoogle Scholar
[17]Tomkinson, M. J., FC-groups (Pitman, Boston, 1984).Google Scholar
[18]Wood, G. J., ‘On pronormal subgroups of finite soluble groups’, Arch. Math. 25 (1974), 578–588.CrossRefGoogle Scholar