A family of non-Schurian p-Schur rings over groups of order p3${p^{3}}$

Abstract

Abstract Recently, it was proved that every commutative p-Schur ring over a group of order p 3 ${p^{3}}$ is Schurian. In this article, we consider the Schurity problem of non-commutative p-Schur rings over groups of order p 3 ${p^{3}}$ . In particular, we give a family of non-Schurian p-Schur rings over groups of order p 3 ${p^{3}}$ .