This paper is devoted to the classification of all flag-transitive point-primitive non-trivial 2-(v,k,λ) designs with the alternating group An(n≤10) as the socle of their automorphism groups, and 87 different designs are obtained up to isomorphism. The results of this study further improve the classification theory of designs under the action of almost simple groups, and provide reference for the follow-up study of similar problems.
@article{arxiv.2508.20716,
title = {Classification of flag-transitive $2$-$(v, k, \lambda)$ designs with alternating group $A_n$($n \le 10$) as socle},
author = {Delu Tian and Qianfen Liao and Zhilin Zhang},
journal= {arXiv preprint arXiv:2508.20716},
year = {2025}
}