JournalsggdVol. 14, No. 3pp. 991–1005

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

  • Eloisa Detomi

    Università di Padova, Italy
  • Marta Morigi

    Università di Bologna, Italy
  • Pavel Shumyatsky

    Universidade de Brasília, Brazil
Words of Engel type are concise in residually finite groups. Part II cover
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Abstract

This work is a natural follow-up of the article [5]. Given a group-word ww and a group GG, the verbal subgroup w(G)w(G) is the one generated by all ww-values in GG. The word ww is called concise if w(G)w(G) is finite whenever the set of ww-values in GG is finite. It is an open question whether every word is concise in residually finite groups. Let w=w(x1,,xk)w=w(x_1,\ldots,x_k) be a multilinear commutator word, nn a positive integer and qq a prime power. In the present article we show that the word [wq,ny][w^q,_ny] is concise in residually finite groups (Theorem 1.2) while the word [w,ny][w,_ny] 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. 991–1005

DOI 10.4171/GGD/571