Almost free groups in varieties. (English. Russian original) Zbl 0799.20030
Math. Notes 51, No. 3, 293-296 (1992); translation from Mat. Zametki 51, No. 3, 101-105 (1992).
The main result of this paper is the following Theorem: Let \(k\) be an uncountable regular cardinal, not weakly compact, and \(\mathcal V\) be an arbitrary variety of groups containing the variety of all abelian groups \(\mathcal A\). Then there exists an almost \(\mathcal V\)-free, but not \(\mathcal V\)- free group of rank \(k\).
Reviewer: D.Busneag (Craiova)
MSC:
| 20E10 | Quasivarieties and varieties of groups |
| 20E05 | Free nonabelian groups |
| 08B20 | Free algebras |
| 20F18 | Nilpotent groups |
| 03E55 | Large cardinals |
Keywords:
Schreier property; variety of abelian groups; almost \(\mathcal V\)-free group; uncountable regular cardinal; variety of groupsReferences:
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