Block-Transitive 3-(v, 5, λ) Designs with Sporadic or Alternating Socle

Authors

Hui Huang School of Science, East China JiaoTong University, Nanchang, 330013, P. R. China
Suyun Ding School of Science, East China JiaoTong University, Nanchang, 330013, P. R. China
Xiaoqin Zhan School of Science, East China JiaoTong University, Nanchang, 330013, P. R. China https://orcid.org/0000-0003-0669-6419

DOI:

https://doi.org/10.37256/cm.6520257693

Keywords:

3-design, block-transitive, automorphism, sporadic group, alternating group

Abstract

This paper presents a systematic classification of 3-designs with block size 5. Let be a nontrivial 3-(v, 5, λ) design, and let G ≤ Aut act transitively on blocks. We classify all such pairs (, G) where the socle of G is either: one of the 26 sporadic simple groups, or an alternating group A_n(n ≥ 5).

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Published

2025-08-26

Issue

Contemporary Mathematics, Volume 6 Issue 5 (2025)

Section

Research Article

License

This work is licensed under a Creative Commons Attribution 4.0 International License.