On Splitting of the Normalizer of a Maximal Torus in E7(q) and E8(q) Full article
| Journal |
Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126 |
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| Output data | Year: 2021, Volume: 31, Number: 4, Pages: 244-282 Pages count : 39 DOI: 10.1134/S1055134421040027 | ||||
| Tags | algebraic normalizer; finite group of Lie type; maximal torus; Weyl group | ||||
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| Affiliations |
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Funding (1)
| 1 | Russian Science Foundation | 14-21-00065 |
Abstract:
Abstract: 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|. © 2021, Pleiades Publishing, Ltd.
Cite:
Galt A.A.
, Staroletov A.M.
On Splitting of the Normalizer of a Maximal Torus in E7(q) and E8(q)
Siberian Advances in Mathematics. 2021. V.31. N4. P.244-282. DOI: 10.1134/S1055134421040027 Scopus OpenAlex
On Splitting of the Normalizer of a Maximal Torus in E7(q) and E8(q)
Siberian Advances in Mathematics. 2021. V.31. N4. P.244-282. DOI: 10.1134/S1055134421040027 Scopus OpenAlex
Identifiers:
| Scopus: | 2-s2.0-85121737856 |
| OpenAlex: | W4285355202 |