Geodesic
The nilpotent $\pi$-length of maximum subgroups in finite $\pi$-soluble groups
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2009), pp. 3-8

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A connection between $\pi$-lengths of a $\pi$-soluble group and its maximal subgroup is established. The results are applied to the corresponding projectors and injectors in soluble groups. 
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     author = {V. S. Monakhov and O. A. Shpyrko},
     title = {The nilpotent $\pi$-length of maximum subgroups in finite $\pi$-soluble groups},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {3--8},
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     number = {6},
     year = {2009},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2009_6_a0/}
}
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V. S. Monakhov; O. A. Shpyrko. The nilpotent $\pi$-length of maximum subgroups in finite $\pi$-soluble groups. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2009), pp. 3-8. http://geodesic.mathdoc.fr/item/VMUMM_2009_6_a0/