J Austral Math Soc Ser A 58 pp134--141, 1995.

On the Number of Subgroups in Finite Solvable Groups

Marcel Herzog and Olaf Manz

(Received 5 October 1990; revised 10 March 1992)

Abstract

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.

1991 AMS Subject Classification: 20D10

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Authors

Marcel Herzog: School of Mathematical Sciences, Raymond and Beverly Sackler Facualty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel.
Olaf Manz: IWR, Universitat Heidelberg, D-6900 Heidleberg, Germany.; UCI, Utility Consultants International, D-6000 Frankfurt 71, Germany.

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Last Modified: Thu Jan 9 9:04:23 2003