On a problem of B. Hartley about a small centralizer in finite and locally finite groups
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918127686647808 |
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| author | Khukhro, Evgeny |
| author_facet | Khukhro, Evgeny |
| contents | It is proved that if a finite group $G$ has an automorphism of order $n$ with $m$ fixed points, then $G$ has a soluble subgroup whose index and Fitting height are bounded in terms of $m$ and $n$. As a corollary, a problem of B. Hartley is solved in the affirmative: if a locally finite group $G$ has an element with finite centralizer, then $G$ has a subgroup of finite index which has a finite normal series with locally nilpotent factors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20999 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a problem of B. Hartley about a small centralizer in finite and locally finite groups Khukhro, Evgeny Group Theory It is proved that if a finite group $G$ has an automorphism of order $n$ with $m$ fixed points, then $G$ has a soluble subgroup whose index and Fitting height are bounded in terms of $m$ and $n$. As a corollary, a problem of B. Hartley is solved in the affirmative: if a locally finite group $G$ has an element with finite centralizer, then $G$ has a subgroup of finite index which has a finite normal series with locally nilpotent factors. |
| title | On a problem of B. Hartley about a small centralizer in finite and locally finite groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2505.20999 |