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On the Existence of Hereditarily G -Permutable Subgroups in Exceptional Groups G of Lie Type. / Galt, A. A.; Tyutyanov, V. N.

In: Siberian Mathematical Journal, Vol. 64, No. 5, 09.2023, p. 1110-1116.

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Galt AA, Tyutyanov VN. On the Existence of Hereditarily G -Permutable Subgroups in Exceptional Groups G of Lie Type. Siberian Mathematical Journal. 2023 Sept;64(5):1110-1116. doi: 10.1134/S003744662305004X

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Galt, A. A. ; Tyutyanov, V. N. / On the Existence of Hereditarily G -Permutable Subgroups in Exceptional Groups G of Lie Type. In: Siberian Mathematical Journal. 2023 ; Vol. 64, No. 5. pp. 1110-1116.

BibTeX

@article{0a87e6159a224884aa434f188955977c,
title = "On the Existence of Hereditarily G -Permutable Subgroups in Exceptional Groups G of Lie Type",
abstract = "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.",
keywords = "512.542, G -permutable subgroup, exceptional group of Lie type, hereditarily G -permutable subgroup",
author = "Galt, {A. A.} and Tyutyanov, {V. N.}",
note = "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.",
year = "2023",
month = sep,
doi = "10.1134/S003744662305004X",
language = "English",
volume = "64",
pages = "1110--1116",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",
number = "5",

}

RIS

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 -

ID: 59280621