发表机构
Great Bay University; Southern University of Science and Technology（大湾区大学; 南方科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文完成了$\mathcal{Q}(4,q)$上具有非可解传递自同构群的BLT集的分类，证明可约情形下只能是经典BLT集或Kantor半域BLT集。
AI 中文摘要
对于奇素数幂$q$，BLT集$\mathcal B$是$\mathcal Q(4,q)$中的$(q+1)$个点的集合，使得$\mathcal Q(4,q)$中的每个点至多与$\mathcal B$中的两个点共线。我们完成了$\mathcal Q(4,q)$上具有非可解传递自同构群的BLT集的分类。Nelson和Penttila完成了在底层$5$维向量空间上不可约作用的非可解传递自同构群的BLT集$\mathcal B$的分类。在本文中，我们证明了具有在底层$5$维向量空间上可约作用的非可解传递全自同构群的BLT集要么是经典BLT集，要么是Kantor半域BLT集。
英文摘要
For an odd prime power $q$, a BLT-set $\mathcal B$ is a set of $(q+1)$ points of $\mathcal Q(4,q)$ such that every point of $\mathcal Q(4,q)$ is collinear with at most two points of $\mathcal B$. We complete the classification of BLT-sets of $\mathcal Q(4,q)$ admitting a non-solvable transitive automorphism group. Nelson and Penttila completed the classification of BLT-sets $\mathcal B$ with a non-solvable transitive automorphism group acting irreducibly on the underlying $5$-dimensional vector space. In this paper, we prove that a BLT-set with a non-solvable transitive full automorphism group acting reducibly on the underlying $5$-dimensional vector space is either a classical BLT-set or a Kantor semifield BLT-set.
Comments33 pages, comments are welcome
