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The Cayley isomorphism property for the group C5 2 × Cp. / Ryabov, Grigory.

In: Ars Mathematica Contemporanea, Vol. 19, No. 2, 2020, p. 277-295.

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

Harvard

Ryabov, G 2020, 'The Cayley isomorphism property for the group C5 2 × Cp', Ars Mathematica Contemporanea, vol. 19, no. 2, pp. 277-295. https://doi.org/10.26493/1855-3974.2348.F42

APA

Ryabov, G. (2020). The Cayley isomorphism property for the group C5 2 × Cp. Ars Mathematica Contemporanea, 19(2), 277-295. https://doi.org/10.26493/1855-3974.2348.F42

Vancouver

Ryabov G. The Cayley isomorphism property for the group C5 2 × Cp. Ars Mathematica Contemporanea. 2020;19(2):277-295. doi: 10.26493/1855-3974.2348.F42

Author

Ryabov, Grigory. / The Cayley isomorphism property for the group C5 2 × Cp. In: Ars Mathematica Contemporanea. 2020 ; Vol. 19, No. 2. pp. 277-295.

BibTeX

@article{8600bfdf5ef34cf0b9ac01f498b3a7e4,
title = "The Cayley isomorphism property for the group C5 2 × Cp",
abstract = "A finite group G is called a DCI-group if two Cayley digraphs over G are isomorphic if and only if their connection sets are conjugate by a group automorphism. We prove that the group C5 2 × Cp, where p is a prime, is a DCI-group if and only if p ≠ 2. Together with the previously obtained results, this implies that a group G of order 32p, where p is a prime, is a DCI-group if and only if p ≠ 2 and G ≅ C5 2 × Cp.",
keywords = "DCI-groups, Isomorphisms, Schur rings, ADAMS CONJECTURE, SCHUR RINGS, ELEMENTARY ABELIAN-GROUP, GRAPHS",
author = "Grigory Ryabov",
note = "Funding Information: ∗The work is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. The author would like to thank Prof. Istv{\'a}n Kov{\'a}cs for the fruitful discussions on the subject matters, Prof. Pablo Spiga and the anonymous referee for valuable comments which help to improve the text significantly. E-mail address: gric2ryabov@gmail.com (Grigory Ryabov) Publisher Copyright: {\textcopyright} 2020 Society of Mathematicians, Physicists and Astronomers of Slovenia. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
doi = "10.26493/1855-3974.2348.F42",
language = "English",
volume = "19",
pages = "277--295",
journal = "Ars Mathematica Contemporanea",
issn = "1855-3966",
publisher = "DMFA Slovenije",
number = "2",

}

RIS

TY - JOUR

T1 - The Cayley isomorphism property for the group C5 2 × Cp

AU - Ryabov, Grigory

N1 - Funding Information: ∗The work is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. The author would like to thank Prof. István Kovács for the fruitful discussions on the subject matters, Prof. Pablo Spiga and the anonymous referee for valuable comments which help to improve the text significantly. E-mail address: gric2ryabov@gmail.com (Grigory Ryabov) Publisher Copyright: © 2020 Society of Mathematicians, Physicists and Astronomers of Slovenia. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020

Y1 - 2020

N2 - A finite group G is called a DCI-group if two Cayley digraphs over G are isomorphic if and only if their connection sets are conjugate by a group automorphism. We prove that the group C5 2 × Cp, where p is a prime, is a DCI-group if and only if p ≠ 2. Together with the previously obtained results, this implies that a group G of order 32p, where p is a prime, is a DCI-group if and only if p ≠ 2 and G ≅ C5 2 × Cp.

AB - A finite group G is called a DCI-group if two Cayley digraphs over G are isomorphic if and only if their connection sets are conjugate by a group automorphism. We prove that the group C5 2 × Cp, where p is a prime, is a DCI-group if and only if p ≠ 2. Together with the previously obtained results, this implies that a group G of order 32p, where p is a prime, is a DCI-group if and only if p ≠ 2 and G ≅ C5 2 × Cp.

KW - DCI-groups

KW - Isomorphisms

KW - Schur rings

KW - ADAMS CONJECTURE

KW - SCHUR RINGS

KW - ELEMENTARY ABELIAN-GROUP

KW - GRAPHS

UR - http://www.scopus.com/inward/record.url?scp=85098535094&partnerID=8YFLogxK

U2 - 10.26493/1855-3974.2348.F42

DO - 10.26493/1855-3974.2348.F42

M3 - Article

AN - SCOPUS:85098535094

VL - 19

SP - 277

EP - 295

JO - Ars Mathematica Contemporanea

JF - Ars Mathematica Contemporanea

SN - 1855-3966

IS - 2

ER -

ID: 27346017