Abstract: An S-ring (a Schur ring) is said to be separable with respect to a class of groups K if every algebraic isomorphism from the S-ring in question to an S-ring over a group from K is induced by a combinatorial isomorphism. A finite group G is said to be separable with respect to K if every S-ring over G is separable with respect to 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.

Cite: Ryabov G.
Separability of Schur Rings Over Abelian Groups of Odd Order
Graphs and Combinatorics. 2020. V.36. N6. P.1891-1911. DOI: 10.1007/s00373-020-02206-4 WOS Scopus OpenAlex

Dates:

Submitted:	Dec 18, 2019
Accepted:	Jun 7, 2020
Published print:	Jul 9, 2020

Identifiers:

Web of science:	WOS:000546832900001
Scopus:	2-s2.0-85087700882
OpenAlex:	W3040767247

Citing: Пока нет цитирований

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