Geodesic
On Finite Groups with $p$-Decomposable Cofactors of Subgroups
Matematičeskie zametki, Tome 92 (2012) no. 3, pp. 440-446.

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It is proved that, for a finite group with $p$-decomposable cofactors of the maximal subgroups, the quotient group by the Fitting subgroup is $p$-decomposable. This implies that every group all of whose maximal subgroups have nilpotent cofactors is metanilpotent.
Keywords: finite group, cofactor of a subgroup, Fitting subgroup, $p$-decomposable subgroup, metanilpotent group. 
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I. V. Lemeshev. On Finite Groups with $p$-Decomposable Cofactors of Subgroups. Matematičeskie zametki, Tome 92 (2012) no. 3, pp. 440-446. http://geodesic.mathdoc.fr/item/MZM_2012_92_3_a11/

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