Geodesic
Dependence of the derived $p$-length of a $p$-solvable group on the order of its Sylow $p$-subgroup
Problemy fiziki, matematiki i tehniki, no. 3 (2014), pp. 58-60

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It is proved that the derived $p$-length $l_p^a(G)$ of the $p$-solvable group $G$ in which the Sylow $p$-subgroup has order $p^n$ is at most $1+\frac n2$ and if $p\not\in\{2,3\}$ then $l_p^a(G)\leqslant\frac{n+1}2$.
Keywords: finite group, Sylow subgroup, derived $p$-length.
Mots-clés : $p$-solvable group 
@article{PFMT_2014_3_a10,
     author = {D. V. Gritsuk},
     title = {Dependence of the derived $p$-length of a $p$-solvable group on the order of its {Sylow} $p$-subgroup},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {58--60},
     publisher = {mathdoc},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2014_3_a10/}
}
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D. V. Gritsuk. Dependence of the derived $p$-length of a $p$-solvable group on the order of its Sylow $p$-subgroup. Problemy fiziki, matematiki i tehniki, no. 3 (2014), pp. 58-60. http://geodesic.mathdoc.fr/item/PFMT_2014_3_a10/