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Separability of Schur Rings Over Abelian Groups of Odd Order. / Ryabov, Grigory.
в: Graphs and Combinatorics, Том 36, № 6, 01.11.2020, стр. 1891-1911.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Separability of Schur Rings Over Abelian Groups of Odd Order
AU - Ryabov, Grigory
N1 - Publisher Copyright: © 2020, Springer Japan KK, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/11/1
Y1 - 2020/11/1
N2 - 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.
AB - 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.
KW - Cayley graph isomorphism problem
KW - Cayley graphs
KW - Schur rings
UR - http://www.scopus.com/inward/record.url?scp=85087700882&partnerID=8YFLogxK
U2 - 10.1007/s00373-020-02206-4
DO - 10.1007/s00373-020-02206-4
M3 - Article
AN - SCOPUS:85087700882
VL - 36
SP - 1891
EP - 1911
JO - Graphs and Combinatorics
JF - Graphs and Combinatorics
SN - 0911-0119
IS - 6
ER -
ID: 24768160