On the existence of hereditarily G-permutable subgroups in exceptional groups G of lie type

On the existence of hereditarily G-permutable subgroups in exceptional groups G of lie type Full article

Journal

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

Output data

Year: 2023, Volume: 64, Number: 5, Pages: 1110–1116 Pages count : 7 DOI: 10.1134/S003744662305004X

Funding (1)

Russian Science Foundation

23-41-10003

A subgroup A of a group G is G-permutable in G if for every subgroup B ≤ G there exists x ∈Gsuch that ABx = BxA. A subgroup A is hereditarily G-permutable in G if A is E-permutable in every subgroup E of G which includes A. The Kourovka Notebook has Problem 17.112(b): Which finite nonabelian simple groups G possess a proper hereditarily G-permutable subgroup? We answer this question for the exceptional groups of Lie type. Moreover, for the Suzuki groups G ∼ =2B2(q)weprove that a proper subgroup of G is G-permutable if and only if the order of the subgroup is 2. In particular, we obtain an infinite series of groups with G-permutable subgroups.

Galt A.A. , Tyutyanov V.N.
On the existence of hereditarily G-permutable subgroups in exceptional groups G of lie type
Siberian Mathematical Journal. 2023. V.64. N5. P.1110–1116. DOI: 10.1134/S003744662305004X WOS Scopus РИНЦ OpenAlex

Гальт А.А. , Тютянов В.Н.
О существовании наследственно G-перестановочных подгрупп в исключительных группах лиева типа
Сибирский математический журнал. 2023. Т.64. №5. С.935-944. DOI: 10.33048/smzh.2023.64.504 РИНЦ

Submitted:	Mar 18, 2023
Accepted:	Aug 2, 2023
Published print:	Sep 26, 2023
Published online:	Sep 26, 2023

Web of science:	WOS:001075048700004
Scopus:	2-s2.0-85172202690
Elibrary:	63366527
OpenAlex:	W4387063104

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