Block Designs with gcd(r, λ)=1 Admitting Flag-Transitive Automorphism Groups

作者：Alavi, Seyed Hassan^*; Bayat, Mohsen; Biliotti, Mauro; Daneshkhah, Ashraf; Francot, Eliana; Guan, Haiyan; Montinaro, Alessandro; Mouseli, Fatemeh; Rizzo, Pierluigi; Tian, Delu; Wang, Yajie; Zhan, Xiaoqin; Zhang, Yongli; Zhou, Shenglin; Zhu, Yan

来源：Results in Mathematics, 2022, 77(4): 151.

DOI：10.1007/s00025-022-01697-2

• 2-design
• flag-transitive
• automorphism group

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 D with gcd(r, lambda) = 1, then either (D, G) is one of the known examples described in this paper, or D has q = p(d) points with p prime and G is a subgroup of A Gamma L-1(q).

• 单位
  广东教育学院; 广东技术师范学院