TY - JOUR

T1 - Characterization of the Group A5 × A5 × A5 by the Set of Conjugacy Class Sizes

AU - Gorshkov, I. b.

AU - Panshin, V. v.

N1 - The study was carried out as part of the state assignment to Sobolev Institute of Mathematics SB RAS, project FWNF-2022-0002.

PY - 2025/1/22

Y1 - 2025/1/22

N2 - For a finite group G, we denote by N (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, and also for S ∈ {A5, A6}, where Ak denotes the alternating group of degree k, with n = 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.

AB - For a finite group G, we denote by N (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, and also for S ∈ {A5, A6}, where Ak denotes the alternating group of degree k, with n = 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.

UR - https://doi.org/10.33048/alglog.2024.63.203

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85217409569&origin=inward&txGid=be4bb413094635de4400f5edaa720458

U2 - 10.1007/s10469-025-09775-4

DO - 10.1007/s10469-025-09775-4

M3 - Article

VL - 63

SP - 105

EP - 113

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 2

ER -