Given a group-word w and a group G, the verbal subgroup w(G) is the onegenerated by all w-values in G. The word w is said to be concise if w(G) isfinite whenever the set of w-values in G is finite. In the sixties P. Hallasked whether every word is concise but later Ivanov answered this question inthe negative. On the other hand, Hall's question remains wide open in the classof residually finite groups. In the present article we show that variousgeneralizations of the Engel word are concise in residually finite groups.
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