2024/04/09 by Costantino Delizia, Delizia, Costantino, Michele Gaeta +3
Arts and Humanities · #Lexicography and Language Studies
paper · pdf · doi:10.48550/arxiv.2404.06308
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.