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A Schunck class construction and a problem concerning primitive groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Peter Förster
Peter Förster
Affiliation:
Department of Mathematics Monash University Clayton, Vic. 3168, Australia
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Abstract

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Gaschütz has introduced the concept of a product of a Schunck class and a (saturated) formation (differing from the usual product of classes) and has shown that this product is a Schunck class provided that both of its factors consist of finite soluble groups. We investigate the same question in the context of arbitrary finite groups.

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 1 , February 1985 , pp. 130 - 137
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Baer, R. and Förster, P., “Einbettungsrelationen und Formationen endlicher Gruppen” (in preparation).Google Scholar
[2]Beidleman, J. G., ‘Formations and π-closure in finite groups’, Compositio Math. 23 (1971), 347–356.Google Scholar
[3]Beidleman, J. G. and Brewster, B., Formations of finite π-closed groups I, II, Boll. Un. Mat. Ital. 4 (1971), 563–575, 651–657.Google Scholar
[4]Erickson, R. P., ‘Products of saturated formations’, Comm. Algebra 10 (1982), 1911–1917.CrossRefGoogle Scholar
[5]Förster, P., ‘Projektive Klassen endlicher Gruppen. I. Schunck- und Gaschützklassen’, Math. Z. 186 (1984), 149–178.CrossRefGoogle Scholar
[6]Gaschütz, W., ‘Lectures on subgroups of Sylow type in finite soluble groups’, Notes on Pure Mathematics 11, Australian National University, Canberra, 1979.Google Scholar
[7]Lafuente, J., ‘Nonabelian crowns and Schunck classes of finite groups’, Arch. Math. (Basel), to appear.Google Scholar
[8]Lausch, H., ‘Formations of π-soluble groups’, J. Austral. Math. Soc. 10 (1969), 241–250.CrossRefGoogle Scholar
[9]Lausch, H., ‘Formations of groups and π-decomposability’, Proc. Amer. Math. Soc., 20 (1969), 203–206.Google Scholar