Geodesic
Stably solvable groups
Izvestiya. Mathematics , Tome 3 (1969) no. 4, pp. 723-736

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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 $s$. 
@article{IM2_1969_3_4_a3,
     author = {D. I. Zaitsev},
     title = {Stably solvable groups},
     journal = {Izvestiya. Mathematics },
     pages = {723--736},
     publisher = {mathdoc},
     volume = {3},
     number = {4},
     year = {1969},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1969_3_4_a3/}
}
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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/