Characterization of the Group A5 × A5 × A5 by the Set of Conjugacy Class Sizes

Characterization of the Group A5 × A5 × A5 by the Set of Conjugacy Class Sizes Full article

Journal

Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302

Output data

Year: 2025, Volume: 63, Number: 2, Pages: 105-113 Pages count : 9 DOI: 10.1007/s10469-025-09775-4

Funding (1)

Sobolev Institute of Mathematics

FWNF-2022-0002

For a finite group G,wedenotebyN(G) the set of its conjugacy class sizes. Recently, the following question was posed: given any n ∈ N and an arbitrary non-Abelian finite simple group S, is it true that G Sn if G is a group with trivial center and N(G)=N(Sn)? The answer to this question is known for all simple groups S with n =1,andalsofor S ∈{A5,A6},whereAk denotes the alternating group of degree k,withn =2. It is proved that the group A5 ×A5 ×A5 is uniquely defined by the set N(A5 ×A5 ×A5) in the class of finite groups with trivial center.

Gorshkov I.B. , Panshin V.V.
Characterization of the Group A5 × A5 × A5 by the Set of Conjugacy Class Sizes
Algebra and Logic. 2025. V.63. N2. P.105-113. DOI: 10.1007/s10469-025-09775-4 WOS Scopus РИНЦ OpenAlex

Горшков И.Б. , Паньшин В.В.
Характеризация группы A5xA5xA5 множеством размеров классов сопряжённых элементов
Алгебра и логика. 2024. Т.63. №2. С.154-166. DOI: 10.33048/alglog.2024.63.203 РИНЦ

Submitted:	Aug 22, 2022
Accepted:	Dec 6, 2024
Published print:	Jan 22, 2025
Published online:	Jan 22, 2025

Web of science:	WOS:001401987800001
Scopus:	2-s2.0-85217409569
Elibrary:	81403759
OpenAlex:	W4406726052

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