Geodesic
On the derived $\pi$-length of a~finite $\pi$-solvable group with a~given $\pi$-Hall subgroup
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 215-223

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Let $G_\pi$ be a $\pi$-Hall subgroup of a finite $\pi$-solvable group $G$, and let $M$ be a maximal subgroup of $G_\pi$. We find estimates for the derived $\pi$-length $l^a_\pi(G)$ of $G$ depending on the structure of the subgroups $G_\pi$ or $M$. We consider the situation where all proper subgroups in these subgroups are abelian or nilpotent. In particular, we prove that $l_\pi^a(G)\le5$ if $M$ is a minimal nonnilpotent group.
Mots-clés : finite $\pi$-solvable group
Keywords: Hall subgroup, derived length. 
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     author = {V. S. Monakhov and D. V. Gritsuk},
     title = {On the derived $\pi$-length of a~finite $\pi$-solvable group with a~given $\pi${-Hall} subgroup},
     journal = {Trudy Instituta matematiki i mehaniki},
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     publisher = {mathdoc},
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     year = {2013},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a21/}
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V. S. Monakhov; D. V. Gritsuk. On the derived $\pi$-length of a~finite $\pi$-solvable group with a~given $\pi$-Hall subgroup. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 215-223. http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a21/