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Schunck classes and projectors in a class of locally finite groups

Published online by Cambridge University Press:  20 January 2009

M. J. Tomkinson
M. J. Tomkinson
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland
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Abstract

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We introduce a definition of a Schunck class of periodic abelian-by-finite soluble groups using major subgroups in place of the maximal subgroups used in Finite groups. This allows us to develop the theory as in the finite case proving the existence and conjugacy of projectors. Saturated formations are examples of Schunck classes and we are also able to obtain an infinite version of Gaschütz Ω-subgroups.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 3 , October 1995 , pp. 511 - 522
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

REFERENCES

1.Doerk, K. and Hawkes, T. O., Finite soluble groups (de Gruyter, 1992).CrossRefGoogle Scholar
2.Gardiner, A. D., Hartley, B. and Tomkinson, M. J., Saturated formations and Sylow structure in locally finite groups. J. Algebr. 17 (1971), 177–211.CrossRefGoogle Scholar
3.Gaschütz, W., Zur Theorie der endlichen auflösbaren Gruppen, Math. Z. 80 (1963), 300–305.CrossRefGoogle Scholar
4.Gaschotz, W., Lectures on subgroups of Sylow type in finite soluble groups (Australian National University, 1979).Google Scholar
5.Hartley, B., A dual approach to Černikov modules, Math. Proc. Cambridge Philos. Soc. 82 (1977), 215–239.CrossRefGoogle Scholar
6.Huppert, B., Endliche Gruppen I (Springer, 1968).Google Scholar
7.Huppert, B. and Blackburn, N., Finite groups II (Springer, 1982).CrossRefGoogle Scholar
8.Schunck, H.ℌ-Untergruppen in endlichen auflösbaren Gruppen., Math. Z. 97 (1967), 326–330.CrossRefGoogle Scholar
9.Tomkinson, M. J., A Frattini-like subgroup, Math. Proc. Cambridge Philos. Soc. 77 (1975), 247–257.CrossRefGoogle Scholar
10.Tomkinson, M. J., Major subgroups of nilpotent-by-finite groups, Ukrain. Mat. Zh. 44 (1992), 853–856.CrossRefGoogle Scholar