Normal structure of isotropic reductive groups over rings

Stavrova, Anastasia; Stepanov, A. P.

doi:10.1016/j.jalgebra.2022.11.014

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2024

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“…In [16] Alexander Luzgarev and Stavrova showed that the elementary subgroup is perfect (under a natural additional assumption). Stavrova and Stepanov also proved [18] that such isotropic reductive groups admit a standard classification of subgroups normalized by the elementary group if the structure constants are invertible in K. For twisted Chevalley groups normality of the elementary subgroup was already proved in [3,21]. See also the survey [23] for details.…”

Section: Introductionmentioning

confidence: 99%

Groups normalized by the odd unitary group

Egor

2020

St. Petersburg Math. J.

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Steinberg pro-groups are certain pro-groups used to analyze ordinary Steinberg groups locally in Zariski topology. In this paper we show that Steinberg pro-groups associated with general linear groups, odd unitary groups, and Chevalley groups satisfy a Zariski cosheaf property as crossed pro-modules over the base groups. Also, we prove an analogue of the standard commutator formulae for relative Steinberg groups. As an application, we show that the base groups over localized rings naturally act on the corresponding Steinberg pro-groups.

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