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arXiv · 2404.06308

A generalization of concise words

Costantino Delizia·Michele Gaeta·Carmine Monetta
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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 $w$ is said to be concise if the verbal subgroup $w(G)$ is finite in each group $G$ in which $w$ 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.

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Costantino Delizia, Michele Gaeta, Carmine Monetta. 2024-04-09. A generalization of concise words. https://doi.org/10.1515/jgth-2024-0148

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