More countably recognizable classes of groups. (English) Zbl 1172.20029
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 \(\mathcal C\). R. Baer [in the article Math. Z. 79, 344-363 (1962; Zbl 0105.25901)] introduced countable recognizability. Series of articles continued its investigation. M. R. Dixon, M. J. Evans and 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.
Reviewer: Igor Subbotin (Los Angeles)
MSC:
| 20F19 | Generalizations of solvable and nilpotent groups |
| 20E25 | Local properties of groups |
| 20E10 | Quasivarieties and varieties of groups |
Keywords:
(locally soluble)-by-finite rank groups; countably recognizable groups; countable subgroups; classes of groupsReferences:
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