On transitive sets of derangements in primitive groups
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909047826939904 |
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| author | Müller, Peter |
| author_facet | Müller, Peter |
| contents | We construct a primitive permutation action of the Steinberg triality group $^3D_4(2)$ of degree $4064256$ and show that there are distinct points $α,β$ such that there is no derangement $g\in{^3D_4}(2)$ with $α^g=β$. This answers a question by John G. Thompson (Problem 8.75 in the Kourovka Notebook) in the negative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_08459 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On transitive sets of derangements in primitive groups Müller, Peter Group Theory 20B15 We construct a primitive permutation action of the Steinberg triality group $^3D_4(2)$ of degree $4064256$ and show that there are distinct points $α,β$ such that there is no derangement $g\in{^3D_4}(2)$ with $α^g=β$. This answers a question by John G. Thompson (Problem 8.75 in the Kourovka Notebook) in the negative. |
| title | On transitive sets of derangements in primitive groups |
| topic | Group Theory 20B15 |
| url | https://arxiv.org/abs/2304.08459 |