The growth of residually soluble groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914146830778368 |
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| author | Eberhard, Sean Maini, Elena |
| author_facet | Eberhard, Sean Maini, Elena |
| contents | Building on work of Wilson, we show that if $G$ is a finitely generated residually soluble group whose growth function $γ$ satisfies $(\log γ(n))/ n^{1/4} \to 0$ as $n \to \infty$ then $G$ is virtually nilpotent. This shows that Grigorchuk's Gap Conjecture holds for all exponents $β< 1/4$ within the class of residually soluble groups (improving Wilson's exponent $1/6$). We also discuss stronger versions of the Gap Conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07018 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The growth of residually soluble groups Eberhard, Sean Maini, Elena Group Theory 20F69, 20F65, 20E26, 20F16 Building on work of Wilson, we show that if $G$ is a finitely generated residually soluble group whose growth function $γ$ satisfies $(\log γ(n))/ n^{1/4} \to 0$ as $n \to \infty$ then $G$ is virtually nilpotent. This shows that Grigorchuk's Gap Conjecture holds for all exponents $β< 1/4$ within the class of residually soluble groups (improving Wilson's exponent $1/6$). We also discuss stronger versions of the Gap Conjecture. |
| title | The growth of residually soluble groups |
| topic | Group Theory 20F69, 20F65, 20E26, 20F16 |
| url | https://arxiv.org/abs/2511.07018 |