Abstract:
The carpet subgroups admitting a Bruhat decomposition and different from Chevalley groups are exhausted by the groups lying between the Chevalley groups of type $B_l$, $C_l$, $F_4$, or $G_2$ over various imperfect fields of exceptional characteristic $2$ or $3$, the larger of which is an algebraic extension of the smaller field. Moreover, as regards the types $B_l$ and $C_l$, these subgroups are parametrized by the pairs of additive subgroups one of which may fail to be a field and, for the type $B_2$, even both additive subgroups may fail to be fields. In this paper for the carpet subgroups admitting a Bruhat decomposition we present the relations similar to those well known for Chevalley groups over fields.
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