On pairs of additive subgroups associated with intermediate subgroups of groups of Lie type over nonperfect fields
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 5, pp. 604-610
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The author has previously (Trudy IMM UrO RAN, 19(2013), no. 3) described the groups lying between twisted Chevalley groups $G(K)$ and $G(F)$ of type $^2A_l$, $^2D_l$, $^2E_6$, $^3D_4$ in the case when the larger field $F$ is an algebraic extension of the smaller nonperfect field $K$ of exceptional characteristic for the group $G(F)$ (characteristics $2$ and $3$ for the type $^3D_4$ and only $2$ for other types). It turned out that apart from, perhaps, the type $^2D_l$, such intermediate subgroups are standard, that is, they are exhausted by the groups $G(P)H$ for some intermediate subfield $P$, $K\subseteq P\subseteq F$, and of the diagonal subgroup $H$ normalizing the group $G(P)$. In this note, it is established that intermediate subgroups are also standard for the type $^2D_l$.
Keywords:
groups of Lie type, nonperfect field, intermediate subgroups, carpet of additive subgroups.
@article{JSFU_2021_14_5_a7,
author = {Yakov N. Nuzhin},
title = {On pairs of additive subgroups associated with intermediate subgroups of groups of {Lie} type over nonperfect fields},
journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
pages = {604--610},
publisher = {mathdoc},
volume = {14},
number = {5},
year = {2021},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JSFU_2021_14_5_a7/}
}
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%0 Journal Article %A Yakov N. Nuzhin %T On pairs of additive subgroups associated with intermediate subgroups of groups of Lie type over nonperfect fields %J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika %D 2021 %P 604-610 %V 14 %N 5 %I mathdoc %U http://geodesic.mathdoc.fr/item/JSFU_2021_14_5_a7/ %G en %F JSFU_2021_14_5_a7
Yakov N. Nuzhin. On pairs of additive subgroups associated with intermediate subgroups of groups of Lie type over nonperfect fields. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 5, pp. 604-610. http://geodesic.mathdoc.fr/item/JSFU_2021_14_5_a7/