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The Fitting Length of a Finite Soluble Group and the Number of Conjugacy Classes of its Maximal Metanilpotent Subgroups

Published online by Cambridge University Press:  20 November 2018

A. R. Makan
A. R. Makan*
Affiliation:
University of Kentucky, Lexington, Kentucky
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It is known that the Fitting length h(G) of a finite soluble group G is bounded in terms of the number v(G) of the conjugacy classes of its maximal nilpotent subgroups. For |G| odd, a bound on h(G) in terms of v(G) was discussed in Lausch and Makan [6]. In the case when the prime 2 divides |G|, a logarithmic bound on h(G) in terms of v(G) is obtained in [7]. The main purpose of this paper is to show that the Fitting length of a finite soluble group is also bounded in terms of the number of conjugacy classes of its maximal metanilpotent subgroups. In fact, our result is rather more general.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 2 , June 1973 , pp. 233 - 237
Copyright
Copyright © Canadian Mathematical Society 1973

References

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