Geodesic
Finite solvable groups in which the Sylow $p$-subgroups are either bicyclic or of order~$p^3$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 2, pp. 121-131

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All groups considered in this paper will be finite. Our main result here is the following theorem. Let $G$ be a solvable group in which the Sylow $p$-subgroups are either bicyclic or of order $p^3$ for any $p\in\pi(G)$. Then the derived length of $G$ is at most 6. In particular, if $G$ is an $\mathrm A_4$- free group, then the following statements are true: (1) $G$ is a dispersive group; (2) if no prime $q\in\pi(G)$ divides $p^2+p+1$ for any prime $p\in\pi(G)$, then $G$ is Ore dispersive; (3) the derived length of $G$ is at most 4. 
@article{FPM_2009_15_2_a4,
     author = {V. S. Monakhov and A. Trofimuk},
     title = {Finite solvable groups in which the {Sylow} $p$-subgroups are either bicyclic or of order~$p^3$},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {121--131},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2009_15_2_a4/}
}
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V. S. Monakhov; A. Trofimuk. Finite solvable groups in which the Sylow $p$-subgroups are either bicyclic or of order~$p^3$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 2, pp. 121-131. http://geodesic.mathdoc.fr/item/FPM_2009_15_2_a4/