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# K1 of Chevalley Groups Are Nilpotent

@inproceedings{Vavilov2001K1OC, title={K1 of Chevalley Groups Are Nilpotent}, author={Nikolai Vavilov}, year={2001} }

- Published 2001

Let Φ be a reduced irreducible root system and R be a commutative ring. We consider the corresponding simply connected Chevalley group G = G(Φ, R) and its elementary subgroup E(Φ, R). When rk(Φ) ≥ 2 it is proven by Suslin and Kopeiko [17], [18], [11] for the classical cases and by Taddei [20] for the exceptional cases, that E(Φ, R) is normal in G(Φ, R), so that one can consider the K1-functor modeled on G:

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