论文标题
双流层的对称性
Symmetries of biplanes
论文作者
论文摘要
在本文中，我们首先使用参数$（v，k，2）$研究biplanes $ \ mathcal {d} $，其中块大小$ k \ in \ in \ {13,16 \} $。这些是无法分类的最小参数值。我们表明，如果$ k = 13 $，则$ \ nathcal {d} $是Aschbacher Biplane或其双翼或$ aut（\ Mathcal {d}）$是订单$ 3 $的订单组的子组。在$ k = 16 $的情况下，我们证明$ | aut（\ Mathcal {d}）| $ divides $ 2^{7} \ cdot 3^{2} {2} \ cdot 5 \ cdot 7 \ cdot 7 \ cdot 11 \ cdot 13 $。我们还提供了一个带有参数$（16,6,2）$的双翼飞机的示例，其中具有旗帜传输和点主要的自动形态亚组，可保留均匀的笛卡尔分解。这促使我们研究了用点数自动形态群体来保存笛卡尔分解的双人。我们证明，这样的自动形态组是仿射类型（如示例中），或者是扭曲的花圈类型。
In this paper, we first study biplanes $\mathcal{D}$ with parameters $(v,k,2)$, where the block size $k\in\{13,16\}$. These are the smallest parameter values for which a classification is not available. We show that if $k=13$, then either $\mathcal{D}$ is the Aschbacher biplane or its dual, or $Aut(\mathcal{D})$ is a subgroup of the cyclic group of order $3$. In the case where $k=16$, we prove that $|Aut(\mathcal{D})|$ divides $2^{7}\cdot 3^{2}\cdot 5\cdot 7\cdot 11\cdot 13$. We also provide an example of a biplane with parameters $(16,6,2)$ with a flag-transitive and point-primitive subgroup of automorphisms preserving a homogeneous cartesian decomposition. This motivated us to study biplanes with point-primitive automorphism groups preserving a cartesian decomposition. We prove that such an automorphism group is either of affine type (as in the example), or twisted wreath type.
