Words of Engel type are concise in residually finite groups. Part II

2019/05/19 by Detomi, Eloisa, Morigi, Marta, Shumyatsky, Pavel
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1905.07784

Abstract

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 called concise if w(G) is finite whenever the set of w-values in G is finite. It is an open question whether every word is concise in residually finite groups. Let w=w(x₁,..,x_k) be a multilinear commutator word, n a positive integer and q a prime power. In the present article we show that the word [w^q,_n y] is concise in residually finite groups while the word [w,_n y] is boundedly concise in residually finite groups.

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