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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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BibTeXRIS

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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