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On minimal Fitting classes of periodic, infinite groups

  • Brendan McCann (a1)

Abstract

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.

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[1]Beidleman, J. C., Karbe, M. J. and Tomkinson, M. J., ‘Fitting classes of -groups, I’, Illinois J. Math. 33 (1989), 333359.
[2]Beidleman, J. C. and Tomkinson, M. J., ‘Hypercentral and nilpotent injectors of -groups’, Comm. Algebra 18 (1990) 43074321.
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[7]McCann, B., ‘Examples of minimal Fitting classes of finite groups’, Arch. Math. 49 (1987), 179186.
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[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. 237252.
[10]Menegazzo, F. and Newell, M. L., ‘Injectors in Fitting Classes of -groups’, to appear.
[11]Robinson, D. J. S., A course in the theory of groups (Springer, Berlin, 1982).
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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