Geodesic
Groups with the Minimal Condition on Non-“Nilpotent-by-Finite” Subgroups
Serdica Mathematical Journal, Tome 28 (2002) no. 2, pp. 153-162.

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We characterize the groups which do not have non-trivial perfect sections and such that any strictly descending chain of non-“nilpotent-by-finite” subgroups is finite.
Keywords: Nilpotent-by-Finite Group, Minimal Non-“Nilpotent-by-Finite” Group, Minimal Condition 
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     author = {Artemovych, O.},
     title = {Groups with the {Minimal} {Condition} on {Non-{\textquotedblleft}Nilpotent-by-Finite{\textquotedblright}} {Subgroups}},
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Artemovych, O. Groups with the Minimal Condition on Non-“Nilpotent-by-Finite” Subgroups. Serdica Mathematical Journal, Tome 28 (2002) no. 2, pp. 153-162. http://geodesic.mathdoc.fr/item/SMJ2_2002_28_2_a3/