305 research outputs found
Words of Engel type are concise in residually finite groups
Given a group-word w and a group G, the verbal subgroup w(G) is the one generated
by all w-values in G. The word w is said to be concise if w(G) is finite whenever the set
of w-values in G is finite. In the sixties P. Hall asked whether every word is concise but
later Ivanov answered this question in the negative. On the other hand, Hall\u2019s question
remains wide open in the class of residually finite groups. In the present article we
show that various generalizations of the Engel word are concise in residually finite
groups
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