Classification of flag-transitive $2$-$(v, k, λ)$ designs with alternating group $A_n$($n \le 10$) as socle
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908508208758784 |
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| author | Tian, Delu Liao, Qianfen Zhang, Zhilin |
| author_facet | Tian, Delu Liao, Qianfen Zhang, Zhilin |
| contents | This paper is devoted to the classification of all flag-transitive point-primitive non-trivial $2$-$(v, k, λ)$ designs with the alternating group $A_n$($n \le 10$) 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_20716 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of flag-transitive $2$-$(v, k, λ)$ designs with alternating group $A_n$($n \le 10$) as socle Tian, Delu Liao, Qianfen Zhang, Zhilin Combinatorics 05B05, 20B25, 20B15, 20B30 This paper is devoted to the classification of all flag-transitive point-primitive non-trivial $2$-$(v, k, λ)$ designs with the alternating group $A_n$($n \le 10$) 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. |
| title | Classification of flag-transitive $2$-$(v, k, λ)$ designs with alternating group $A_n$($n \le 10$) as socle |
| topic | Combinatorics 05B05, 20B25, 20B15, 20B30 |
| url | https://arxiv.org/abs/2508.20716 |