Geodesic
Groups with the weak minimal condition for non-subnormal subgroups II
Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 4, pp. 601-605.

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Let $G$ be a group with the property that there are no infinite descending chains of non-subnormal subgroups of $G$ for which all successive indices are infinite. The main result is that if $G$ is a locally (soluble-by-finite) group with this property then either $G$ has {\it all\/} subgroups subnormal or $G$ is a soluble-by-finite minimax group. This result fills a gap left in an earlier paper by the same authors on groups with the stated property.
Classification : 20E15, 20F19, 20F22
Keywords: subnormal subgroups; soluble-by-finite groups 
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Kurdachenko, Leonid A.; Smith, Howard. Groups with the weak minimal condition for non-subnormal subgroups II. Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 4, pp. 601-605. http://geodesic.mathdoc.fr/item/CMUC_2005__46_4_a1/