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 is said to be concise if the verbal subgroup is finite in each group in which 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.
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}
}