Year: 2026
Type: preprint
Abstract: A group word $w$ is said to be strongly concise in a class $\mathcal{C}$ of profinite groups if, for every group $G \in \mathcal{C}$ such that $w$ takes less than $2^{\aleph_0}$ 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.
Source: arXiv (Cornell University)
Author: Zozaya, Andoni
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7172408159
Cites:
Cited by:
Related to: