论文标题
关于双翼飞机的自动形态组（121,16,2）
On automorphism groups of a biplane (121,16,2)
论文作者
论文摘要
具有参数$（121,16,2）$的双翼飞机的存在是一个开放问题。最近，Alavi，Daneshkhah和Praeger证明了一个可能的Biplane $ {\ Mathcal d} $ of Ardermem of Automorthism of to $ {\ Mathcal d} $ $ 14 $ $ 14 $ divides $ 2^7 \ cdot3^2 \ cdot5 \ cdot5 \ cdot7 \ cdot7 \ cdot11 \ cdot11 \ cdot13 $。在本文中，我们表明，这种双翼飞机没有订单$ 11 $或$ 13 $的自动形态，从而确定$ | aut（{\ nathcal d}）| $划分$ 2^7 \ cdot3^2 \ cdot5 \ cdot7 $ cdot7 $。参数$（121,16,2）$。
The existence of a biplane with parameters $(121,16,2)$ is an open problem. Recently, it has been proved by Alavi, Daneshkhah and Praeger that the order of an automorphism group of a of possible biplane ${\mathcal D}$ of order $14$ divides $2^7\cdot3^2\cdot5\cdot7\cdot11\cdot13$. In this paper we show that such a biplane do not have an automorphism of order $11$ or $13$, and thereby establish that $|Aut({\mathcal D})|$ divides $2^7\cdot3^2\cdot5\cdot7.$ Further, we study a possible action of an automorphism of order five or seven, and some small groups of order divisible by five or seven, on a biplane with parameters $(121,16,2)$.
