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

Hui Huang; Suyun Ding; Xiaoqin Zhan

doi:10.37256/cm.6520257693

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

How to Cite

Huang H, Ding S, Zhan X. Block-Transitive 3-(v, 5, λ) Designs with Sporadic or Alternating Socle. Contemp. Math. [Internet]. 2025 Aug. 26 [cited 2026 Jun. 13];6(5):5466-73. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/7693

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Issue

Contemporary Mathematics, Volume 6 Issue 5 (2025), 5368-7533

Section

Research Article

License

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