Geodesic
The Fitting Length of a Finite Soluble Group and the Number of Conjugacy Classes of its Maximal Metanilpotent Subgroups
Canadian mathematical bulletin, Tome 16 (1973) no. 2, pp. 233-237

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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. 
Makan, A. R. The Fitting Length of a Finite Soluble Group and the Number of Conjugacy Classes of its Maximal Metanilpotent Subgroups. Canadian mathematical bulletin, Tome 16 (1973) no. 2, pp. 233-237. doi: 10.4153/CMB-1973-040-3
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     title = {The {Fitting} {Length} of a {Finite} {Soluble} {Group} and the {Number} of {Conjugacy} {Classes} of its {Maximal} {Metanilpotent} {Subgroups}},
     journal = {Canadian mathematical bulletin},
     pages = {233--237},
     year = {1973},
     volume = {16},
     number = {2},
     doi = {10.4153/CMB-1973-040-3},
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