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arXiv · 2506.17216

The full automorphism groups of the five symmetric $(15,8,4)$-designs

Mark Pankov·Krzysztof Petelczyc·Mariusz Żynel
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Abstract

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.

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Mark Pankov, Krzysztof Petelczyc, Mariusz Żynel. 2025-07-14. The full automorphism groups of the five symmetric $(15,8,4)$-designs. https://arxiv.org/abs/2506.17216

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