Rank One Groups
The notion of a rank one group with abelian unipotent subgroups grew out of the necessity to generalize the concept of k-root subgroups of [Tim91] to the demands of quadratic pairs [Tim99]. It is clear that it is not sufficient just to allow SL2s for this purpose, since other types of “rank one groups”, for example 2-dimensional classical groups of Witt index 1, arise in the situation of quadratic pairs.
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