Elementary Subgroups of Isotropic Reductive Groups
نویسنده
چکیده
Let G be a not necessarily split reductive group scheme over a commutative ring R with 1. Given a parabolic subgroup P of G, the elementary group EP (R) is defined to be the subgroup of G(R) generated by UP (R) and UP−(R), where UP and UP− are the unipotent radicals of P and its opposite P −, respectively. It is proved that if G contains a Zariski locally split torus of rank 2, then the group EP (R) = E(R) does not depend on P , and, in particular, is normal in G(R).
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