Local-global principle for General Quadratic and General Hermitian groups and the nilpotence of KH_1

In this article we establish an analog of the Quillen—Suslin’s local-global principle for the elementary subgroup of the general quadratic group and the general Hermitian group. We show that unstable $\text{k}$-groups of general Hermitian groups over module finite rings are nilpotent-by-abelian. This generalizes earlier results of A. Bak, R. Hazrat, and N. Vavilov.