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arXiv · 2302.12285

The structure of $3$-pyramidal groups

Xiaofang Gao·Martino Garonzi
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Abstract

A combinatorial block design $D$ is called $3$-pyramidal if there exists a subgroup $G$ of $\mbox{Aut}(D)$ fixing $3$ points and acting regularly on the other points. If this happens, we say that the design is $3$-pyramidal under $G$. In case $D$ is a Kirkman triple system, it is known that such a group $G$ has precisely $3$ involutions, all conjugate to each other. In this paper, we obtain a classification of the groups with this property.

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Xiaofang Gao, Martino Garonzi. 2023-02-23. The structure of $3$-pyramidal groups. https://arxiv.org/abs/2302.12285

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