The schurity of association schemes has been studied in many papers. One of the major topics is to investigate the schurity of those association schemes whose thin residues are thin. A difficult case is that the thin residue is an elementary abelian p-group of rank 2. A class of these association schemes has played an important role in the study of p-schemes of order \(p^3\). In this paper, we study the automorphism groups and schurity problem of this class of association schemes. In particular, we will establish very simple sufficient (and necessary) conditions for these association schemes to be schurian. As an application, we obtain two infinite families of schurian association schemes.

在许多论文中都研究了关联方案的准确性。主要主题之一是研究残基稀薄的那些关联方案的安全性。一个困难的情况是薄的残基是一个基本阿贝尔p秩2的一类这些结合方案的-基团起到了研究中的一个重要的作用p的顺序-schemes \（P ^ 3 \） 。在本文中，我们研究了这类关联方案的自同构群和置换问题。特别是，我们将为这些关联方案建立一个非常简单的充分（和必要）条件。作为一个应用程序，我们获得了两个无限的schurian关联计划族。