Geodesic
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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - Yakov N. Nuzhin
TI  - On pairs of additive subgroups associated with intermediate subgroups of groups of Lie type over nonperfect fields
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2021
SP  - 604
EP  - 610
VL  - 14
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2021_14_5_a7/
LA  - en
ID  - JSFU_2021_14_5_a7
ER  - 
%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/