The full automorphism groups of the five symmetric $(15,8,4)$-designs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909687824252928 |
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| author | Pankov, Mark Petelczyc, Krzysztof Żynel, Mariusz |
| author_facet | Pankov, Mark Petelczyc, Krzysztof Żynel, Mariusz |
| contents | It is clear that the full automorphism group of the $(15,8,4)$-design of points and hyperplane complements of ${\rm PG}(3,2)$ is ${\rm GL}(4,2)$. Using methods of point-line geometries, we determine the full automorphism groups of the remaining four symmetric $(15,8,4)$-designs and describe their actions on the sets of points and blocks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17216 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The full automorphism groups of the five symmetric $(15,8,4)$-designs Pankov, Mark Petelczyc, Krzysztof Żynel, Mariusz Combinatorics It is clear that the full automorphism group of the $(15,8,4)$-design of points and hyperplane complements of ${\rm PG}(3,2)$ is ${\rm GL}(4,2)$. Using methods of point-line geometries, we determine the full automorphism groups of the remaining four symmetric $(15,8,4)$-designs and describe their actions on the sets of points and blocks. |
| title | The full automorphism groups of the five symmetric $(15,8,4)$-designs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.17216 |