On generalisations of conciseness
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912591189639168 |
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| author | Zozaya, Andoni |
| author_facet | Zozaya, Andoni |
| contents | 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 $[w(G), G, \stackrel{(m)}{\dots}, G]$ is finite for some $m \in \mathbb{N}$ if and only if $[w(G), G]$ is finite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07012 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On generalisations of conciseness Zozaya, Andoni Group Theory 20F10 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 $[w(G), G, \stackrel{(m)}{\dots}, G]$ is finite for some $m \in \mathbb{N}$ if and only if $[w(G), G]$ is finite. |
| title | On generalisations of conciseness |
| topic | Group Theory 20F10 |
| url | https://arxiv.org/abs/2508.07012 |