论文标题
在$ {\ rm at4}（p，p，p+2，r）$ - 图形的自动形态组的质谱上
On the prime spectrum of an automorphism group of an ${\rm AT4}(p,p+2,r)$-graph
论文作者
论文摘要
本文致力于$ {\ rm at4}的分类问题（p，p，p+2，r）$ - 图。有一个唯一的$ {\ rm at4}（p，p+2，r）$ - $ p = 2 $，即带有距离传播的soicher图，带有相交阵列$ \ {56、45、16、1; 1、8、8、45、45、56 \} $，其本地图是Isomorphic to Gewirtz的图形。是否存在$ {\ rm at4}（p，p，p+2，r）$ - $ p> 2 $的图仍然不知道。每个$ {\ rm at4}的本地图（p，p+2，r）$ - 图非常规定，带有参数$（（p+2）（p^2+4p+2），p（p+3），p-2，p）$。在本文中，我们找到了具有此类参数的强大图形的自动形态组的质谱的上限，并且我们还获得了质量频谱的一些限制，以及$ {\ rm at4}的自动形态组的结构（p，p，p，p，p+2，r）$ p Prime P $是Prime Police prime Power的限制。作为推论，我们表明没有弧传递$ {\ rm at4}（p，p，p+2，r）$ - 带有$ p \ in \ in \ {11,17,27 \} $的图形。
This paper is devoted to the problem of classification of ${\rm AT4}(p,p+2,r)$-graphs. There is a unique ${\rm AT4}(p,p+2,r)$-graph with $p=2$, namely, the distance-transitive Soicher graph with intersection array $\{56, 45, 16, 1;1, 8, 45, 56\}$, whose local graphs are isomorphic to the Gewirtz graph. It is still unknown whether an ${\rm AT4}(p,p+2,r)$-graph with $p>2$ exists. The local graphs of each ${\rm AT4}(p,p+2,r)$-graph are strongly regular with parameters $((p+2)(p^2+4p+2),p(p+3),p-2,p)$. In the present paper, we find an upper bound for the prime spectrum of an automorphism group of a strongly regular graph with such parameters, and we also obtain some restrictions for the prime spectrum and the structure of an automorphism group of an ${\rm AT4}(p,p+2,r)$-graph in case when $p$ is a prime power. As a corollary, we show that there are no arc-transitive ${\rm AT4}(p,p+2,r)$-graphs with $p\in \{11,17,27\}$.
