Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T08:56:06.562Z Has data issue: false hasContentIssue false
  • English
  • Français

On minimal Fitting classes of periodic, infinite groups

Part of: Representation theory of groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Brendan McCann
Brendan McCann
Affiliation:
Department of Physical and Quantitative Sciences, Regional Technical College, Cork Road, Waterford, Ireland
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.

Examples of Fitting classes generated by certain periodic infinite groups are presented in this paper. The groups in question are finite extensions of direct products of quasi-cyclic (Prüfer) groups and are, in particular, Černikov groups. The methods applied follow closely those used for constructing Fitting classes of finite groups, especially in the case of nilpotent length three.

MSC classification

Secondary: 20F16: Solvable groups, supersolvable groups 20F17: Formations of groups, Fitting classes 20D35: Subnormal subgroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 54 , Issue 3 , June 1993 , pp. 304 - 320
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Beidleman, J. C., Karbe, M. J. and Tomkinson, M. J., ‘Fitting classes of -groups, I’, Illinois J. Math. 33 (1989), 333–359.CrossRefGoogle Scholar
[2]Beidleman, J. C. and Tomkinson, M. J., ‘Hypercentral and nilpotent injectors of -groups’, Comm. Algebra 18 (1990) 4307–4321.CrossRefGoogle Scholar
[3]Bryce, R. A., ‘The fitting class generated by a finite soluble group’, (A. N. U. Math. Research Report Series, No. 34, 1988).Google Scholar
[4]Bryce, R. A., Cossey, J. and Ormerod, E. A., ‘Fitting classes after Dark’, in: Group Theory-Proceedings of the Singapore group theory conference, 1987 (eds. Cheng, N. K. and Leong, Y. K.) (de Gruyter, Berlin, 1989) pp. 293–321.Google Scholar
[5]Dark, R. S., ‘Some examples in the theory of injectors of finite soluble groups’, Math. Z. 127 (1972), 145–156.CrossRefGoogle Scholar
[6]Huppert, B., Endliche Gruppen I (Springer, Berlin 1967).CrossRefGoogle Scholar
[7]McCann, B., ‘Examples of minimal Fitting classes of finite groups’, Arch. Math. 49 (1987), 179–186.CrossRefGoogle Scholar
[8]McCann, B., ‘A Fitting class construction’, Ann. Mat. Pura Appl. 157 (1990), 27–61.CrossRefGoogle Scholar
[9]McCann, B., ‘Examples of normal products of finite groups and an application to Fitting classes’, in: Proc. Int. Group Theory Conf., Bressanone/Brixen, 1989 (Supp. ai Rend. del Circolo Mat. di Palermo, Serie II, No. 23, 1990) pp. 237–252.Google Scholar
[10]Menegazzo, F. and Newell, M. L., ‘Injectors in Fitting Classes of -groups’, to appear.Google Scholar
[11]Robinson, D. J. S., A course in the theory of groups (Springer, Berlin, 1982).CrossRefGoogle Scholar