Geodesic
Derived $\pi$-length of a $\pi$-solvable group in which the Sylow $p$-subgroups are either bicyclic or of order~$p^3$
Problemy fiziki, matematiki i tehniki, no. 2 (2014), pp. 54-58

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The group is called a bicyclic group if it is the product of two cyclic subgroups. It is proved that the derived $\pi$-length of the $\pi$-solvable groups in which the Sylow $p$-subgroups are either bicyclic or of order $p^3$ for any $p\in\pi$ is at most 7 and if $2\not\in\pi$ then the derived $\pi$-length is at most 4.
Keywords: finite group, bicyclic group, Sylow subgroup, derived $\pi$-length.
Mots-clés : $\pi$-solvable group 
@article{PFMT_2014_2_a8,
     author = {D. V. Gritsuk},
     title = {Derived $\pi$-length of a $\pi$-solvable group in which the {Sylow} $p$-subgroups are either bicyclic or of order~$p^3$},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {54--58},
     publisher = {mathdoc},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2014_2_a8/}
}
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D. V. Gritsuk. Derived $\pi$-length of a $\pi$-solvable group in which the Sylow $p$-subgroups are either bicyclic or of order~$p^3$. Problemy fiziki, matematiki i tehniki, no. 2 (2014), pp. 54-58. http://geodesic.mathdoc.fr/item/PFMT_2014_2_a8/