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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

1. Carter, R. W. and Hawkes, T.O., The F-normalizers of a finite soluble group, J. Algebra 5 (1967), 175–202.Google Scholar
2. Chambers, G. A., On f-Prefrattini Subgroups, Canad. Math. Bull. 15 (1972), 345–348.Google Scholar
3. Fischer, B.,Gaschütz, W. and Hartley, B., Injektoren endlicher auflösbarer Gruppen, Math. Z. 102 (1967), 337–339.Google Scholar
4. Gaschütz, W., Zur Théorie der endlichen auflösbaren Gruppen, Math. Z. 80 (1963), 300–305.Google Scholar
5. Hartley, B., On Fischer’s dualization of formation theory, Proc. London Math. Soc. (3) 19 (1969), 193–207.Google Scholar
6. Lausch, H. and Makan, A., On a relation between the Fitting length of a soluble group and the number ofconjugacy classes of its maximal nilpotent subgroups, Bull. Austral. Math. Soc. 1 (1969), 3–10.Google Scholar
7. Makan, A. R., On some aspects of finite soluble groups, Ph.D. thesis, The Australian National University, Canberra, April 1971.Google Scholar
8. Wright, C. R. B., On screens and L-Izers of finite solvable groups, Math. Z. 115 (1970), 273–282.Google Scholar