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| 摘要: |
| 研究区传递2-设计的分类是置换群与组合设计领域中的重要课题之一.目前关于区传递2-设计的分类主要集中在自同构群具有旗传递性和点本原性上.本文研究了区本原2-(v,k,λ)对称设计的分类问题,并证明了当设计的点数不大于200且自同构群不为仿射型时,在同构意义下只存在54个这样的设计. |
| 关键词: 区本原 自同构群 对称设计 几乎单型 乘积型 |
| DOI： |
| 分类号:O152.1 |
| 基金项目:国家自然科学基金资助(12361004);江西省自然科学基金资助(20224BAB211005,20242BAB25005). |
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| THE CLASSIFICATION OF BLOCK-PRIMITIVE SYMMETRIC DESIGNS WITH SMALL POINTS NUMBER |
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ZHAN Li-wen,ZHAN Xiao-qin
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| Abstract: |
| The study of the classiflcation of block-transitive 2-designs is one of the important topics in the fleld of permutation group and combinatorial designs. At persent, the classiflcation of block-transitive 2-designs mainly focuses on the flag-transitivity and point-primitivity. In this article, we study the classiflcation of block-primitive 2-(v,k,λ) symmetric designs, and prove the following result: Let D be a 2-(v,k,λ) symmetric design with v · 200, and G be a block-primitive automorphism group of D. If G is not of a–ne type, then up to isomorphism there are only 54 such designs. |
| Key words: Block-primitive automorphism symmetric design almost simple product type |
