2021/08/25 by E. I. Khukhro, Khukhro, E. I., Pavel Shumyatsky +1 · 2 citations
Computer Science · Social Sciences · #Coding theory and cryptography #FOS: Mathematics #Group Theory (math.GR) #Multilingual Education and Policy #semigroups and automata theory
paper · doi:10.48550/arxiv.2108.11789
openalex publication_date 2021/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A group word w is said to be strongly concise in a class \mathscr C of profinite groups if, for any group G in \mathscr C, either w takes at least continuum values in G or the verbal subgroup w(G) is finite. It is conjectured that all words are strongly concise in the class of all profinite groups. Earlier Detomi, Klopsch, and Shumyatsky proved this conjecture for multilinear commutator words, as well as for some other particular words. They also proved that every group word is strongly concise in the class of nilpotent profinite groups. In the present paper we prove that for any n the n-Engel word [...[x,y],y],… y] (where y is repeated n times) is strongly concise in the class of finitely generated profinite groups.