结合方案上Sylow p-子集的若干性质研究

Research on Some Properties of Sylow p-Subsets on Association Schemes

本文主要研究结合方案上Sylow p-子集(p是素数)的若干性质,并利用Sylow p-子集的存在性判断结合方案是非本原的。此外,利用Sylow定理分析价为6和200的结合方案的数学结构,给出价为6的结合方案至少存在一个价为2和3的闭子集,价为200的结合方案至少存在一个价为2、4、5、8和25的闭子集。

In this paper, we study some properties of Sylow p-subset (p is a prime number) on association schemes, and the existence of Sylow p-subset is used to judge that the association scheme is imprimitive. Sylow theorem is used to analyze the mathematical structure of the association schemes with valency 6 and 200. The association scheme of valency 6 has at least one closed subset with valency 2 and 3. And the association scheme of valency 200 has at least one closed subset with valency 2, 4, 5, 8 and 25.