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.
On generalized concise words
Delizia C.
;Gaeta M.;Monetta C.
2025
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.File in questo prodotto:
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