Geodesic
Stably solvable groups
Izvestiya. Mathematics, Tome 3 (1969) no. 4, pp. 723-736 
D. I. Zaitsev. Stably solvable groups. Izvestiya. Mathematics, Tome 3 (1969) no. 4, pp. 723-736. http://geodesic.mathdoc.fr/item/IM2_1969_3_4_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that in the class of radical groups containing solvable subgroups of some class $s$, the descending chain condition for subgroups is equivalent to the descending chain condition for solvable subgroups of class $s$.

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[4] Hall Ph., “On the finiteness of certain soluble groups”, Proc. London Math. Soc., 9 (1959), 595–622 | DOI | MR | Zbl

[5] Polovitskii Ya. D., “O gruppakh s usloviem $\pi$-minimalnosti dlya podgrupp”, Sib. matem. zh., 3:4 (1964), 582–591

[6] Kurosh A. G., Teoriya grupp, Gostekhizdat, M., 1953 | MR