This work is a natural follow-up of the article . Given a group-word and a group , the verbal subgroup is the one generated by all -values in . The word is called concise if is finite whenever the set of -values in is finite. It is an open question whether every word is concise in residually finite groups. Let be a multilinear commutator word, a positive integer and a prime power. In the present article we show that the word is concise in residually finite groups (Theorem 1.2) while the word is boundedly concise in residually finite groups (Theorem 1.1).
Cite this article
Eloisa Detomi, Marta Morigi, Pavel Shumyatsky, Words of Engel type are concise in residually finite groups. Part II. Groups Geom. Dyn. 14 (2020), no. 3, pp. 991–1005DOI 10.4171/GGD/571