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The Cayley isomorphism property for the group C5 2 × Cp. / Ryabov, Grigory.
в: Ars Mathematica Contemporanea, Том 19, № 2, 2020, стр. 277-295.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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