DOI

Abstract. This is a continuation of the study of subgroups of the Chevalley group GP (Φ, R) over a ring R with root system Φ and weight lattice P that contain the elementary subgroup EP (Φ, K) over a subring K of R. A. Bak and A. V. Stepanov considered recently the case of the symplectic group (simply connected group with root system Φ = Cl) in characteristic 2. In the current article, that result is extended to the case of Φ = Bl and for the groups with other weight lattices. Like in the Ya. N. Nuzhin's work on the case where R is an algebraic extension of a nonperfect field K and Φ is not simply laced, the description involves carpet subgroups parametrized by two additive subgroups. In the second part of the article, the Bruhat decomposition is established for these carpet subgroups and it is proved that they have a split saturated Tits system. As a corollary, it is shown that they are simple as abstract groups.
Original languageEnglish
Pages (from-to)719-737
Number of pages19
JournalSt. Petersburg Mathematical Journal
Volume31
Issue number4
DOIs
StatePublished - 1 Jan 2020

    Research areas

  • Bruhat decomposition, Carpet subgroups, Classical groups, Subgroup lattice

ID: 127603863