On exceptional Lie geometries

On exceptional compact homogeneous geometries of type C3

We provide a uniform framework to study the exceptional homogeneous compact geometries of type C3. This framework is then used to show that these are simply connected, answering a question by Kramer and Lytchak, and to calculate the full automorphism groups.

直线与反对在例外型李 incidence 几何中的研究

Lines and Opposition in Lie Incidence Geometries of Exceptional Type

本文研究了例外型李 incidence 几何中直线的性质，通过反对关系定义几何线，并将其与最小阻挡集联系起来。

旗传递点本原拟对称2-设计与例外李型群

Flag-transitive point-primitive quasi-symmetric $2$-designs and exceptional groups of Lie type

本文研究具有特定块相交数的非平凡拟对称2-设计的旗传递点本原自同构群，证明其基柱不可能是有限单例外李型群，推进了相关分类问题。

Flag-transitive block designs and finite exceptional simple groups of Lie type

In this article, we study $2$-designs with $\gcd(r,λ)=1$ admitting a flag-transitive almost simple automorphism group with socle a finite simple exceptional group of Lie type. We obtain four infinite families of such designs and provide some examples in each of these families.

Flag-transitive non-symmetric $2$-designs with $(r,λ)=1$ and exceptional groups of Lie type

This paper determined all pairs $(\mathcal{D},G)$ where $\mathcal{D}$ is a non-symmetric 2-$(v,k,λ)$ design with $(r,λ)=1$ and $G$ is the almost simple flag-transitive automorphism group of $\mathcal{D}$ with an exceptional socle of Lie type. We prove that if $T\trianglelefteq G\leq Aut(T)$ where $T$ is an exceptional group of Lie type, then $T$ must be the Ree group or Suzuki group, and there are five classes of non-isomorphic designs $\mathcal{D}$.

区传递t-(k²,k,λ)设计与李型单例外群

Block-transitive t-(k^2,k,\lam) designs and simple exceptional groups of Lie type

针对非平凡t-(k²,k,λ)设计的区传递自同构群G，证明其基柱不可能为有限李型单例外群，为该类设计的自同构群结构研究提供关键结论。