Toward a Sharp Baer–Suzuki Theorem for the pi-Radical: Unipotent Elements of Groups of Lie Type

Toward a Sharp Baer–Suzuki Theorem for the pi-Radical: Unipotent Elements of Groups of Lie Type Full article

Journal

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

Output data

Year: 2024, Volume: 62, Number: 6, Pages: 476-500 Pages count : 25 DOI: 10.1007/s10469-024-09760-3

Funding (1)

Sobolev Institute of Mathematics

FWNF-2022-0002

We will look into the following conjecture, which, if valid, would allow us to formulate an unimprovable analog of the Baer–Suzuki theorem for the π-radical of a finite group (here π is an arbitrary set of primes). For an odd prime number r,putm = r, ifr =3, and m=r−1 if r ⩾5.LetL be a simple non-Abelian group whose order has a prime divisor s such that s = r if r divides |L| and s>r otherwise. Suppose also that x is an automorphism of prime order of L. Then some m conjugates of x in the group L,x generate a subgroup of order divisible by s. The conjecture is confirmed for the case where L is a group of Lie type and x is an automorphism induced by a unipotent element.

Liu A-M. , Wang Z. , Revin D.O.
Toward a Sharp Baer–Suzuki Theorem for the pi-Radical: Unipotent Elements of Groups of Lie Type
Algebra and Logic. 2024. V.62. N6. P.476-500. DOI: 10.1007/s10469-024-09760-3 WOS Scopus РИНЦ OpenAlex

Лю А.-М. , Ван Ч. , Ревин Д.О.
К точной теореме Бэра–Сузуки для π-радикала: унипотентные элементы групп лиева типа
Алгебра и логика. 2023. Т.62. №6. С.708-741. DOI: 10.33048/alglog.2023.62.602 РИНЦ

Submitted:	Dec 6, 2023
Accepted:	Dec 2, 2024
Published print:	Dec 21, 2024
Published online:	Dec 21, 2024

Web of science:	WOS:001382501400001
Scopus:	2-s2.0-85212857519
Elibrary:	80170704
OpenAlex:	W4405655468

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