Geodesic
Verbally closed subgroups of free solvable groups
Algebra i logika, Tome 59 (2020) no. 3, pp. 367-384.

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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.
Keywords: free solvable group, verbally closed subgroup, $l$-verbally closed subgroup. 
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V. A. Roman'kov; E. I. Timoshenko. Verbally closed subgroups of free solvable groups. Algebra i logika, Tome 59 (2020) no. 3, pp. 367-384. http://geodesic.mathdoc.fr/item/AL_2020_59_3_a6/

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