On a conjecture of Peter Neumann on fixed points in permutation groups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918330142556160 |
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| author | Garzoni, Daniele Guralnick, Robert M. Liebeck, Martin W. |
| author_facet | Garzoni, Daniele Guralnick, Robert M. Liebeck, Martin W. |
| contents | We prove a conjecture of Peter Neumann from 1966, predicting that every finite non-regular primitive permutation group of degree $n$ contains an element fixing at least one point and at most $n^{1/2}$ points. In fact, we prove a stronger version, where $n^{1/2}$ is replaced by $n^{1/3}$, and this is best possible. The case where $G$ is affine was proved by Guralnick and Malle; in this paper we address the case where $G$ is non-affine. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03832 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a conjecture of Peter Neumann on fixed points in permutation groups Garzoni, Daniele Guralnick, Robert M. Liebeck, Martin W. Group Theory 20B15, 20D05 We prove a conjecture of Peter Neumann from 1966, predicting that every finite non-regular primitive permutation group of degree $n$ contains an element fixing at least one point and at most $n^{1/2}$ points. In fact, we prove a stronger version, where $n^{1/2}$ is replaced by $n^{1/3}$, and this is best possible. The case where $G$ is affine was proved by Guralnick and Malle; in this paper we address the case where $G$ is non-affine. |
| title | On a conjecture of Peter Neumann on fixed points in permutation groups |
| topic | Group Theory 20B15, 20D05 |
| url | https://arxiv.org/abs/2602.03832 |