TY - JOUR

T1 - On Splitting of the Normalizer of a Maximal Torus in E7(q) and E8(q)

AU - Galt, A. A.

AU - Staroletov, A. M.

N1 - Funding Information: The work was partially supported by the Russian Scientific Foundation (project no. 14-21-00065). Publisher Copyright: © 2021, Pleiades Publishing, Ltd.

PY - 2021/10

Y1 - 2021/10

N2 - Let G be a finite group of Lie type E7(q) or E8(q) over a field Fq and let W be the Weyl group of G. In the present article, we find all maximal tori T of the group G that admit complements in the algebraicnormalizer N(G, T). For every group under consideration except forthe simply connected group E7(q), we provethe following assertion: If (Formula presented.) and the corresponding torus T lacks the complementthen there exists a lift of w in N(G, T) of order |w|. In the exceptional case, we find all elements w admitting a lift in N(G, T) of order |w|.

AB - Let G be a finite group of Lie type E7(q) or E8(q) over a field Fq and let W be the Weyl group of G. In the present article, we find all maximal tori T of the group G that admit complements in the algebraicnormalizer N(G, T). For every group under consideration except forthe simply connected group E7(q), we provethe following assertion: If (Formula presented.) and the corresponding torus T lacks the complementthen there exists a lift of w in N(G, T) of order |w|. In the exceptional case, we find all elements w admitting a lift in N(G, T) of order |w|.

KW - algebraic normalizer

KW - finite group of Lie type

KW - maximal torus

KW - Weyl group

UR - http://www.scopus.com/inward/record.url?scp=85121737856&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=47550219

UR - https://www.mendeley.com/catalogue/3f553174-d93b-3c35-9d15-ef7d79c5e2a7/

U2 - 10.1134/S1055134421040027

DO - 10.1134/S1055134421040027

M3 - Article

AN - SCOPUS:85121737856

VL - 31

SP - 244

EP - 282

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 4

M1 - 2

ER -