The nilpotent \pi-length of maximum subgroups in finite \pi-soluble groups / V. S. Monakhov, O. A. Shpyrko. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2009. ? 6. P.  [Moscow Univ. Math. Bulletin. Vol. 64, N 6, 2009. P. ].

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.

Key words: finite soluble group, maximal subgroup, nilpotent length, projector, injector.