Eparability of Schur Rings Over an Abelian Group of Order 4p

Abstract

An S-ring (a Schur ring) is said to be separable with respect to a class of groups if every its algebraic isomorphism to an S-ring over a group from is induced by a combinatorial isomorphism. It is proved that every Schur ring over an Abelian group G of order 4p, where p is a prime, is separable with respect to the class of Abelian groups. This implies that the Weisfeiler-Lehman dimension of the class of Cayley graphs over G is at most 3.