Strong conciseness in profinite metabelian groups

2026/08/03 by Andoni Zozaya
Mathematics · #math.GR #msc:20F10 #msc:20F16 #msc:20F18 #msc:20E18 #msc:20E22

paper · pdf

15 pages

arxiv created 2026/08/03 · arxiv updated 2026/08/04

Abstract

A group word w is said to be strongly concise in a class C of profinite groups if, for every group G ∈ C such that w takes less than 2^ℵ₀ values in G, the verbal subgroup w(G) is finite. Using the notion of polynomial mappings introduced by Passi, we establish that every group word is strongly concise in the class of profinite metabelian groups. With this new approach, we also give an alternative proof for the fact that every group word is strongly concise in the class of profinite nilpotent groups.

Citations

• Conciseness of first-order formulae
• Strong conciseness and equationally Noetherian groups
• Conciseness of compact R-analytic groups
• Strong conciseness of Engel words in profinite groups
• Strong conciseness of coprime and anti-coprime commutators
• On countable coverings of word values in profinite groups
• Polynomial functors from Algebras over a set-operad and non-linear Mackey functors