TY - JOUR

T1 - On the Existence of Hereditarily G -Permutable Subgroups in Exceptional Groups G of Lie Type

AU - Galt, A. A.

AU - Tyutyanov, V. N.

N1 - The work was supported by a joint grant of the Belorussian Republican Foundation for Fundamental Research (Project F23RSF-237) and the Russian Science Foundation No. 23-41-10003, https://rscf.ru/en/project/23-41-10003/. Публикация для корректировки.

PY - 2023/9

Y1 - 2023/9

N2 - A subgroup A of a group G is G -permutable in G if forevery subgroup B\leq G there exists x\in G such that AB^{x}=B^{x}A . 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 properhereditarily G -permutable subgroup? We answer this questionfor the exceptional groups of Lie type. Moreover, for the Suzuki groups G\cong{{}^{2}\!\operatorname{B}_{2}}(q) we prove 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.

AB - A subgroup A of a group G is G -permutable in G if forevery subgroup B\leq G there exists x\in G such that AB^{x}=B^{x}A . 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 properhereditarily G -permutable subgroup? We answer this questionfor the exceptional groups of Lie type. Moreover, for the Suzuki groups G\cong{{}^{2}\!\operatorname{B}_{2}}(q) we prove 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.

KW - 512.542

KW - G -permutable subgroup

KW - exceptional group of Lie type

KW - hereditarily G -permutable subgroup

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85172202690&origin=inward&txGid=284d75eb8f2899530e6bf44de722a769

UR - https://www.mendeley.com/catalogue/75d53a3f-7e3d-3276-bce2-bc461d98bcd9/

U2 - 10.1134/S003744662305004X

DO - 10.1134/S003744662305004X

M3 - Article

VL - 64

SP - 1110

EP - 1116

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 5

ER -