Profinite groups with soluble centralisers
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917680675553280 |
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| author | Shumyatsky, Pavel Thillaisundaram, Anitha |
| author_facet | Shumyatsky, Pavel Thillaisundaram, Anitha |
| contents | We show that a profinite group, in which the centralisers of non-trivial elements are metabelian, is either virtually pro-$p$ or virtually soluble of derived length at most 4. We furthermore show that a prosoluble group, in which the centralisers of non-trivial elements are soluble of bounded derived length, is either soluble or virtually pro-$p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20964 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Profinite groups with soluble centralisers Shumyatsky, Pavel Thillaisundaram, Anitha Group Theory We show that a profinite group, in which the centralisers of non-trivial elements are metabelian, is either virtually pro-$p$ or virtually soluble of derived length at most 4. We furthermore show that a prosoluble group, in which the centralisers of non-trivial elements are soluble of bounded derived length, is either soluble or virtually pro-$p$. |
| title | Profinite groups with soluble centralisers |
| topic | Group Theory |
| url | https://arxiv.org/abs/2405.20964 |