More countably recognizable classes of groups.
A class \(\mathcal C\) of groups is countably recognizable if \(G\in\mathcal C\) for every group \(G\) that has all countable subgroups lying in \(\mathcal C\). \textit{R. Baer} [in the article Math. Z. 79, 344-363 (1962; Zbl 0105.25901)] introduced countable recognizability. Series of articles continued its investigation. \textit{M. R. Dixon, M. J. Evans} and \textit{H. Smith} [in the paper J. Group Theory 10, No. 5, 641-653 (2007; Zbl 1129.20018)] proved that certain important class extensions are countably recognizable. In the interesting article under review, the author proves that certain classes of groups that are either (locally soluble)-by-finite rank or finite rank-by-(locally soluble) are countably recognizable.
scientific article; zbMATH DE number 5544386