The Strong π-Sylow Theorem for the Groups PSL_2(q)

The Strong π-Sylow Theorem for the Groups PSL_2(q) Full article

Journal

Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260

Output data

Year: 2024, Volume: 65, Number: 5, Pages: 1187–1194 Pages count : 8 DOI: 10.1134/S0037446624050173

Funding (1)

Russian Science Foundation

24-21-00163

Let π be a set of primes. A finite group G is a π-group if all prime divisors of the order of G belong to π. Following Wielandt, the π-Sylow theorem holds for G if all maximal π-subgroups of G are conjugate; if the π-Sylow theorem holds for every subgroup of G then the strong π-Sylow theorem holds for G. The strong π-Sylow theorem is known to hold for G if and only if it holds for every nonabelian composition factor of G. In 1979, Wielandt asked which finite simple nonabelian groups obey the strong π-Sylow theorem. By now the answer is known for sporadic and alternating groups. We give some arithmetic criterion for the validity of the strong π-Sylow theorem for the groups PSL2(q).

Revin D.O. , Shepelev V.D.
The Strong π-Sylow Theorem for the Groups PSL_2(q)
Siberian Mathematical Journal. 2024. V.65. N5. P.1187–1194. DOI: 10.1134/S0037446624050173 WOS Scopus РИНЦ OpenAlex

Ревин Д.О. , Шепелев В.Д.
Сильная π-теорема Силова для групп PSL_2(q)
Сибирский математический журнал. 2024. Т.65. №5. С.1011-1021. DOI: 10.33048/smzh.2024.65.517 РИНЦ

Submitted:	Apr 10, 2024
Accepted:	Jun 20, 2024
Published print:	Sep 25, 2024
Published online:	Sep 25, 2024

Web of science:	WOS:001320442300006
Scopus:	2-s2.0-85204874304
Elibrary:	69920893
OpenAlex:	W4402842401

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