Block-transitive Steiner 4-design with an almost simple automorphism group(具有几乎单型自同构群的区传递Steiner 4-设计)
The classification of block-transitive t-design is a very interesting and important problem in the field of finite group and block design. The classification of block-transitive 2-design has been fully studied. But when t is greater than 3, the classification of block-transitive t-designs is still a...
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Zhejiang University Press
2025-07-01
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| Series: | Zhejiang Daxue xuebao. Lixue ban |
| Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2025.04.001 |
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| author | 龚罗中(GONG Luozhong) 曾玲玲(ZENG Lingling) |
| author_facet | 龚罗中(GONG Luozhong) 曾玲玲(ZENG Lingling) |
| author_sort | 龚罗中(GONG Luozhong) |
| collection | DOAJ |
| description | The classification of block-transitive t-design is a very interesting and important problem in the field of finite group and block design. The classification of block-transitive 2-design has been fully studied. But when t is greater than 3, the classification of block-transitive t-designs is still an open problem. In this paper, the classification problem of block transitive 4-designs is studied using the results of the classification of 2-homogeneous permutation groups. It is shown that if a Steiner 4-design admits an almost simple block-transitive automorphism group G, then G is either a typical simple group or G=M11 and D is a 4-(11,5,1) design or G=M23 and D is a 4-(23,7,1) design.区传递t-设计的分类是有限群与区组设计研究领域非常有趣且重要的问题。对区传递2-设计的分类已有比较充分的研究，但对t≥3的区传递t-设计的分类研究较少。利用2-齐次置换群的分类结论，研究了区传递4-设计的分类问题，证明了如果Steiner 4-设计D具有几乎单型区传递自同构群G，则要么G是典型单群，要么G=M11且D是4-(11,5,1)设计，或者G=M23且D是4-(23,7,1)设计。 |
| format | Article |
| id | doaj-art-e9128e65039241c08192cb2d279252c8 |
| institution | Kabale University |
| issn | 1008-9497 |
| language | zho |
| publishDate | 2025-07-01 |
| publisher | Zhejiang University Press |
| record_format | Article |
| series | Zhejiang Daxue xuebao. Lixue ban |
| spelling | doaj-art-e9128e65039241c08192cb2d279252c82025-08-20T03:40:43ZzhoZhejiang University PressZhejiang Daxue xuebao. Lixue ban1008-94972025-07-0152441942310.3785/j.issn.1008-9497.2025.04.001Block-transitive Steiner 4-design with an almost simple automorphism group(具有几乎单型自同构群的区传递Steiner 4-设计)龚罗中(GONG Luozhong)0https://orcid.org/0000-0003-2435-8632曾玲玲(ZENG Lingling)11School of Mathematics Science， Changsha Normal University， Changsha 410100， China(1长沙师范学院 数学科学学院，湖南 长沙 410100)2Library， Changsha Normal University， Changsha 410100， China(2长沙师范学院 图书馆，湖南 长沙 410100)The classification of block-transitive t-design is a very interesting and important problem in the field of finite group and block design. The classification of block-transitive 2-design has been fully studied. But when t is greater than 3, the classification of block-transitive t-designs is still an open problem. In this paper, the classification problem of block transitive 4-designs is studied using the results of the classification of 2-homogeneous permutation groups. It is shown that if a Steiner 4-design admits an almost simple block-transitive automorphism group G, then G is either a typical simple group or G=M11 and D is a 4-(11,5,1) design or G=M23 and D is a 4-(23,7,1) design.区传递t-设计的分类是有限群与区组设计研究领域非常有趣且重要的问题。对区传递2-设计的分类已有比较充分的研究，但对t≥3的区传递t-设计的分类研究较少。利用2-齐次置换群的分类结论，研究了区传递4-设计的分类问题，证明了如果Steiner 4-设计D具有几乎单型区传递自同构群G，则要么G是典型单群，要么G=M11且D是4-(11,5,1)设计，或者G=M23且D是4-(23,7,1)设计。https://doi.org/10.3785/j.issn.1008-9497.2025.04.001 |
| spellingShingle | 龚罗中(GONG Luozhong) 曾玲玲(ZENG Lingling) Block-transitive Steiner 4-design with an almost simple automorphism group(具有几乎单型自同构群的区传递Steiner 4-设计) Zhejiang Daxue xuebao. Lixue ban |
| title | Block-transitive Steiner 4-design with an almost simple automorphism group(具有几乎单型自同构群的区传递Steiner 4-设计) |
| title_full | Block-transitive Steiner 4-design with an almost simple automorphism group(具有几乎单型自同构群的区传递Steiner 4-设计) |
| title_fullStr | Block-transitive Steiner 4-design with an almost simple automorphism group(具有几乎单型自同构群的区传递Steiner 4-设计) |
| title_full_unstemmed | Block-transitive Steiner 4-design with an almost simple automorphism group(具有几乎单型自同构群的区传递Steiner 4-设计) |
| title_short | Block-transitive Steiner 4-design with an almost simple automorphism group(具有几乎单型自同构群的区传递Steiner 4-设计) |
| title_sort | block transitive steiner 4 design with an almost simple automorphism group 具有几乎单型自同构群的区传递steiner 4 设计 |
| url | https://doi.org/10.3785/j.issn.1008-9497.2025.04.001 |
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