Schurity of association schemes whose thin residues are elementary abelian p-groups of rank 2

Abstract

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.