The Baer–Suzuki width of a complete class of finite group is finite

The Baer–Suzuki width of a complete class of finite group is finite Full article

Journal

St. Petersburg Mathematical Journal
ISSN: 1061-0022 , E-ISSN: 1547-7371

Output data

Year: 2026, Volume: 37, Number: 1, DOI: 10.1090/spmj/1896

Authors

Revin D. ^1,2

Affiliations

1	Novosibirsk State University, ul. Pirogova 1, 630090, Novosibirsk
2	Sobolev Institute of Mathematics, SB RAS, Academician Koptyug avenue 4, 630090, Novosibirsk, Russia

Funding (1)

Russian Science Foundation

24-11-00127

Abstract. Let X be a nonempty class of finite groups closed under taking subgroups, homomorphic images, and extensions. According to Gordeev, Grunewald, Kunyavski˘ı, and Plotkin, the Baer–Suzuki width BS(X )ofX does not exceed a nonnegative integer m if, in any finite group G, the largestnormalX-subgroup coincides with the set of elements x such that every m elements conjugate to x generate an X-subgroup. If there are no m for which BS(X ) ≤ m, then by definition BS(X)=∞. In the paper, it is proved that BS(X ) < ∞ for every class X with the above properties. More precisely, if X is distinct from the class of all finite groups, then the value of BS(X ) does not exceed max{11,2Υ+1} where Υ is equal to the largest n such that Symn ∈ X .

Revin D.
The Baer–Suzuki width of a complete class of finite group is finite
St. Petersburg Mathematical Journal. 2026. V.37. N1. DOI: 10.1090/spmj/1896

Ревин Д.О.
Ширина Бэра-Сузуки полного класса конечных групп конечна
Алгебра и анализ. 2025. Т.37. №1. С.141-176. РИНЦ MathNet

Submitted:	Aug 16, 2024
Published online:	Sep 30, 2026

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