Geodesic
Local-global principle for general quadratic and general Hermitian groups and the nilpotence of~$\mathrm{KH}_1$
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 30, Tome 452 (2016), pp. 5-31

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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 $\mathrm K_1$-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. 
@article{ZNSL_2016_452_a0,
     author = {R. Basu},
     title = {Local-global principle for general quadratic and general {Hermitian} groups and the nilpotence of~$\mathrm{KH}_1$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--31},
     publisher = {mathdoc},
     volume = {452},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_452_a0/}
}
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R. Basu. Local-global principle for general quadratic and general Hermitian groups and the nilpotence of~$\mathrm{KH}_1$. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 30, Tome 452 (2016), pp. 5-31. http://geodesic.mathdoc.fr/item/ZNSL_2016_452_a0/