On p-Schur Rings Over Abelian Groups of Order p³

Abstract

In the theory of Schur rings, it is known that every Schur ring over a cyclic p-group is Schurian. Recently, Spiga and Wang showed that every p-Schur ring over an elementary abelian p-group of rank 3 is Schurian. In this paper, we prove that every p-Schur ring over an abelian group of order p ³ is Schurian.

Key Words:

• Cayley scheme
• p-Schur ring
• Schurian

2010 Mathematics Subject Classification:

• 20C05
• 20B25

ACKNOWLEDGMENTS

The author would like to thank Pablo Spiga for giving valuable comments on the first draft of this paper. He also thanks anonymous referees for their valuable comments.

Notes

Communicated by P. Tiep.