English

A generalization of concise words

Group Theory 2025-11-03 v1

Abstract

The study of verbal subgroups within a group is well-known for being an effective tool to obtain structural information about a group. Therefore, conditions that allow the classification of words in a free group are of paramount importance. One of the most studied problems is to establish which words are concise, where a word ww is said to be concise if the verbal subgroup w(G)w(G) is finite in each group GG in which ww takes only a finite number of values. The purpose of this article is to present some results, in which a hierarchy among words is introduced, generalizing the concept of concise word.

Keywords

Cite

@article{arxiv.2404.06308,
  title  = {A generalization of concise words},
  author = {Costantino Delizia and Michele Gaeta and Carmine Monetta},
  journal= {arXiv preprint arXiv:2404.06308},
  year   = {2025}
}
R2 v1 2026-06-28T15:48:47.929Z