On pairs of additive subgroups associated with intermediate subgroups of groups of Lie type over nonperfect fields

Yakov N. Nuzhin

Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract: 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.

UDC: 512.54

Received: 06.03.2021
Received in revised form: 20.04.2021
Accepted: 24.06.2021

Language: English

DOI: 10.17516/1997-1397-2021-14-5-604-610

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