On A-Groups with the Same Index Set as a Nilpotent Group | Sciact - Система учета научной деятельности ИМ СО РАН

On A-Groups with the Same Index Set as a Nilpotent Group Научная публикация

Журнал

Journal of Algebra
ISSN: 0021-8693 , E-ISSN: 1090-266X

Вых. Данные

Год: 2026, Том: 686, Страницы: 836-844 Страниц : 9 DOI: 10.1016/j.jalgebra.2025.09.003

Ключевые слова

Finite group, A-group, Conjugacy class

Авторы

Zhou Wei ¹ , Gorshkov Ilya ^2,3

Организации

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

Информация о финансировании (1)

Министерство науки и высшего образования РФ

075-15-2025-348

Let G be a finite group and N(G) be the set of conjugacy class sizes of G. For a prime p, let |G||p be the highest p-power dividing some element of N(G) and define |G|| = Πp∈π(G)|G||p. G is said to be an A-group if all its Sylow subgroups are abelian. We prove that if G is an A-group such that N(G) contains |G||p for every p ∈ π(G) as well as |G||, then G must be abelian. This result gives a positive answer to a question posed by Camina and Camina in 2006

Zhou W. , Gorshkov I.
On A-Groups with the Same Index Set as a Nilpotent Group
Journal of Algebra. 2026. V.686. P.836-844. DOI: 10.1016/j.jalgebra.2025.09.003 Scopus

Поступила в редакцию:	20 июн. 2025 г.
Опубликована online:	17 сент. 2025 г.
Опубликована в печати:	15 янв. 2026 г.

Scopus:

2-s2.0-105016144998

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