Verbally closed subgroups of free solvable groups. (English. Russian original) Zbl 1484.20047
Algebra Logic 59, No. 3, 253-265 (2020); translation from Algebra Logika 59, No. 3, 367-384 (2020).
Summary: We establish a series of results on verbally closed and \(l\)-verbally closed subgroups of free solvable groups; here \(l\) is a natural number and the concept of \(l\)-verbal closedness is a generalization of the concept of verbal closedness corresponding to the value \(l = 1\). Under certain assumptions, these subgroups turn out to be retracts and, consequently, are algebraically closed.
MSC:
| 20E07 | Subgroup theorems; subgroup growth |
| 20E05 | Free nonabelian groups |
| 20F16 | Solvable groups, supersolvable groups |
| 20E10 | Quasivarieties and varieties of groups |
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