Geodesic
Bruhat decomposition for carpet subgroups of Chevalley groups over fields
Algebra i logika, Tome 60 (2021) no. 5, pp. 497-509.

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Necessary and sufficient conditions for a Bruhat decomposition to exist in a carpet subgroup of the Chevalley group over a field defined by an irreducible closed carpet of additive subgroups are established. It turns out that carpet subgroups, which admit the Bruhat decomposition and are distinct from Chevalley groups, are exhausted by groups lying between Chevalley groups of types $B_l$, $C_l$, $F_4$ or $G_2$ over various imperfect fields of exceptional characteristics $2$ or $3$, respectively, of which the larger field is an algebraic extension of the smaller field.
Keywords: Bruhat decomposition, Chevalley group, carpet subgroup. 
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Ya. N. Nuzhin; A. V. Stepanov. Bruhat decomposition for carpet subgroups of Chevalley groups over fields. Algebra i logika, Tome 60 (2021) no. 5, pp. 497-509. http://geodesic.mathdoc.fr/item/AL_2021_60_5_a2/

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