arXiv · 2204.02439
Block designs with $\gcd(r,\lambda)=1$ admitting flag-transitive automorphism groups
Abstract
In this paper, we present a classification of $2$-designs with $\gcd(r,\lambda)=1$ admitting flag-transitive automorphism groups. If $G$ is a flag-transitive automorphism group of a non-trivial $2$-design $\mathcal{D}$ with $\gcd(r,\lambda)=1$, then either $(\mathcal{D},G)$ is one of the known examples described in this paper, or $\mathcal{D}$ has $q = p^{d}$ points with $p$ prime and $G$ is a subgroup of $A\Gamma L_{1}(q)$.
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Seyed Hassan Alavi, Mohsen Bayat, Mauro Biliotti, Ashraf Daneshkhah, Eliana Francot, Haiyan Guan, Alessandro Montinaro, Fatemeh Mouseli, Pierluigi Rizzo, Delu Tian, Yajie Wang, Xiaoqin Zhan, Yongli Zhang, Shenglin Zhou, Yan Zhu. 2022-04-05. Block designs with $\gcd(r,\lambda)=1$ admitting flag-transitive automorphism groups. https://arxiv.org/abs/2204.02439
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