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On CI-property of normal Cayley digraphs over abelian groups Научная публикация

Журнал

Journal of Algebra and its Applications
ISSN: 0219-4988

Вых. Данные

Год: 2025, Том: Online ready, Номер статьи : 2750070, Страниц : 23 DOI: 10.1142/s0219498827500708

Ключевые слова

Cayley digraphs; Cayley isomorphism property, Schur rings.

Авторы

Ryabov Grigory ^1,2

Организации

1	School of Mathematical Sciences Hebei Key Laboratory of Computational Mathematics and Applications Hebei Normal University
2	Novosibirsk State Technical University

A Cayley digraph Γ over a finite group G is said to be CI if for every Cayley digraph Γ′ over G isomorphic to Γ, there is an isomorphism from Γ to Γ′ which is at the same time an automorphism of G. In this paper, we study a CI-property of normal Cayley digraphs over abelian groups, i.e. such Cayley digraphs Γ that the group Gr of all right translations of G is normal in Aut(Γ). At first, we reduce the case of an arbitrary abelian group to the case of an abelian p-group. Further, we obtain several results on CI-property of normal Cayley digraphs over abelian p-groups. In particular, we prove that every normal Cayley digraph over an abelian p-group of order at most p5,wherep is an odd prime, is CI.

Ryabov G.
On CI-property of normal Cayley digraphs over abelian groups
Journal of Algebra and its Applications. 2025. V.Online ready. 2750070 :1-23. DOI: 10.1142/s0219498827500708 WOS Scopus OpenAlex

Поступила в редакцию:	2 мар. 2025 г.
Принята к публикации:	9 окт. 2025 г.
Опубликована online:	19 нояб. 2025 г.

Web of science:	WOS:001618654800001
Scopus:	2-s2.0-105022663033
OpenAlex:	W4415737472

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