TY - JOUR

T1 - Splitting of Normalizers of Maximal Tori in Finite Groups of Lie Type

AU - Galt, A. A.

AU - Staroletov, A. M.

N1 - A.A. Galt and A.M. Staroletov are supported by the Program of Fundamental Research RAS, project FWNF-2022-0002. Публикация для корректировки.

PY - 2023/3

Y1 - 2023/3

N2 - Let G be a finite group of Lie type, and T some maximal torus of the group G. We bring to a close the study of the question of whether there exists a complement for a torus T in its algebraic normalizer N (G, T). It is proved that any maximal torus of a group G ∈ {G 2(q), 2 G 2(q), 3 D 4(q)} has a complement in its algebraic normalizer. Also we consider the remaining twisted classical groups 2 An(q) and 2 Dn(q).

AB - Let G be a finite group of Lie type, and T some maximal torus of the group G. We bring to a close the study of the question of whether there exists a complement for a torus T in its algebraic normalizer N (G, T). It is proved that any maximal torus of a group G ∈ {G 2(q), 2 G 2(q), 3 D 4(q)} has a complement in its algebraic normalizer. Also we consider the remaining twisted classical groups 2 An(q) and 2 Dn(q).

KW - Weyl group

KW - algebraic normalizer

KW - finite group of Lie type

KW - maximal torus

KW - twisted group of Lie type

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85181461759&origin=inward&txGid=7086c24dd743f3b0f7415fa68008de2a

UR - https://www.mendeley.com/catalogue/f40572a3-6b00-389f-9d0a-982442871372/

U2 - 10.1007/s10469-023-09721-2

DO - 10.1007/s10469-023-09721-2

M3 - Article

VL - 62

SP - 22

EP - 40

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 1

ER -