Separability of Schur Rings Over Abelian Groups of Odd Order

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Separability of Schur Rings Over Abelian Groups of Odd Order. / Ryabov, Grigory.

In: Graphs and Combinatorics, Vol. 36, No. 6, 01.11.2020, p. 1891-1911.

Research output: Contribution to journal › Article › peer-review

Harvard

Ryabov, G 2020, 'Separability of Schur Rings Over Abelian Groups of Odd Order', Graphs and Combinatorics, vol. 36, no. 6, pp. 1891-1911. https://doi.org/10.1007/s00373-020-02206-4

APA

Ryabov, G. (2020). Separability of Schur Rings Over Abelian Groups of Odd Order. Graphs and Combinatorics, 36(6), 1891-1911. https://doi.org/10.1007/s00373-020-02206-4

Vancouver

Ryabov G. Separability of Schur Rings Over Abelian Groups of Odd Order. Graphs and Combinatorics. 2020 Nov 1;36(6):1891-1911. doi: 10.1007/s00373-020-02206-4

Author

Ryabov, Grigory. / Separability of Schur Rings Over Abelian Groups of Odd Order. In: Graphs and Combinatorics. 2020 ; Vol. 36, No. 6. pp. 1891-1911.

BibTeX

@article{57fb7008ac0f4c0ebe7c220e522c7f61,

title = "Separability of Schur Rings Over Abelian Groups of Odd Order",

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.",

keywords = "Cayley graph isomorphism problem, Cayley graphs, Schur rings",

author = "Grigory Ryabov",

year = "2020",

month = nov,

day = "1",

doi = "10.1007/s00373-020-02206-4",

language = "English",

volume = "36",

pages = "1891--1911",

journal = "Graphs and Combinatorics",

issn = "0911-0119",

publisher = "Springer Japan",

number = "6",

}

RIS

TY - JOUR

T1 - Separability of Schur Rings Over Abelian Groups of Odd Order

AU - Ryabov, Grigory

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