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On the number of subgroups in finite solvable groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Marcel Herzog  and
Olaf Manz
Marcel Herzog
Affiliation:
School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel
Olaf Manz
Affiliation:
IWR, Universität Heidelberg, D-6900 Heidelberg, Germany, and UCI Utility Consultants International, D-6000 Frankfurt 71, Germany
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Abstract

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The main result of this paper is an upper bound for the number of maximal subgroups in finite solvable groups. Our result improves an earlier one of Cook, Wiegold and Williamson [1]. At the end, we use our bound to deduce an estimation for the total number of subgroups in finite solvable groups.

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 58 , Issue 1 , February 1995 , pp. 134 - 141
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Cook, R. J., Wiegold, J. and Williamson, A. G., ‘Enumerating subgroups’, J. Austral. Math. Soc. (Series A) 43 (1987), 220–223.CrossRefGoogle Scholar
[2]Gaschütz, W., ‘Die Eulersche Funktion endlicher auflösbarer Gruppen’, Illinois J. Math. 3 (1959), 469–476.Google Scholar
[3]Gaschütz, W., ‘Präfrattinigruppen’, Arch. Math. 13 (1962), 418–426.Google Scholar