A generalization of concise words
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866918179783049216 |
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| author | Delizia, Costantino Gaeta, Michele Monetta, Carmine |
| author_facet | Delizia, Costantino Gaeta, Michele Monetta, Carmine |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06308 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A generalization of concise words Delizia, Costantino Gaeta, Michele Monetta, Carmine Group Theory 20F10, 20F12, 20F14, 20F24 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. |
| title | A generalization of concise words |
| topic | Group Theory 20F10, 20F12, 20F14, 20F24 |
| url | https://arxiv.org/abs/2404.06308 |