On generalisations of conciseness
Based on the notions of conciseness and semiconciseness, we show that these properties are not equivalent by proving that a word originally presented by Ol’shanskii is semiconcise but not concise. We further establish that every 1/m-concise word is semiconcise by proving that when the group-word w t...
| Autor: | |
|---|---|
| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2025 |
| País: | España |
| Recursos: | Universidad Pública de Navarra |
| Repositorio: | Academica-e. Repositorio Institucional de la Universidad Pública de Navarra |
| OAI Identifier: | oai:academica-e.unavarra.es:2454/55374 |
| Acesso em linha: | https://hdl.handle.net/2454/55374 |
| Access Level: | acceso abierto |
| Palavra-chave: | Group word Verbal subgroup Conciseness Semiconciseness |
| Resumo: | Based on the notions of conciseness and semiconciseness, we show that these properties are not equivalent by proving that a word originally presented by Ol’shanskii is semiconcise but not concise. We further establish that every 1/m-concise word is semiconcise by proving that when the group-word w takes finitely many values in G, the iterated commutator subgroup [w(G), G, (m) ...,G] is finite for some m ∈ N if and only if [w(G), G] is finite. |
|---|