Geodesic
The derived $\pi$-length, nilpotent $\pi$-length, and simple $\pi$-length of finite $\pi$-soluble groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 5, pp. 225-235 
O. A. Shpyrko. The derived $\pi$-length, nilpotent $\pi$-length, and simple $\pi$-length of finite $\pi$-soluble groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 5, pp. 225-235. http://geodesic.mathdoc.fr/item/FPM_2012_17_5_a14/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The concept of the derived $\pi$-length for finite $\pi$-soluble groups is introduced and its elementary properties are described. The dependence between the $\pi$-length, nilpotent $\pi$-length, and derived $\pi$-length, and also between the derived and nilpotent lengths of a $\pi$-Hall subgroup is determined.

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