An S-ring (a Schur ring) is said to be separable with respect to a class of groups \({\mathcal {K}}\) if every algebraic isomorphism from the S-ring in question to an S-ring over a group from \({\mathcal {K}}\) is induced by a combinatorial isomorphism. A finite group G is said to be separable with respect to \({\mathcal {K}}\) if every S-ring over G is separable with respect to \({\mathcal {K}}\). We prove that every abelian group G of order 9p, where p is a prime, is separable with respect to the class of all finite abelian groups. Modulo previously obtained results, this completes a classification of noncyclic abelian groups of odd order that are separable with respect to the class of all finite abelian groups. This also implies that the relative Weisfeiler–Leman dimension of a Cayley graph over G with respect to the class of all Cayley graphs over abelian groups is at most 2.

一个小号-环（一舒尔环）被说成是可分离相对于一类基团的\（{\ mathcal {K}} \）如果从每一个同构代数小号所讨论形圈到小号形环在\（{\ mathcal {K}} \）中的基团是由组合同构引起的。有限群G ^据说是可分离相对于\（{\ mathcal {K}} \）如果每一个小号型圈上ģ是可分离相对于\（{\ mathcal {K}} \） 。我们证明每个阶9 p的阿贝尔群G，其中p是素数，相对于所有有限阿贝尔群的类是可分离的。模数先前获得的结果，这完成了关于所有有限阿贝尔群的类是可分离的奇数阶非循环阿贝尔群的分类。这也意味着相对于阿贝尔群上所有Cayley图的类，G上Cayley图的相对Weisfeiler-Leman维数最多为2。