## Abstract

Let Φ be a reduced irreducible root system and R be a commutative ring. Further, let G(Φ, R) be a Chevalley group of type Φ over R and E(Φ, R) be its elementary subgroup. We prove that if the rank of Φ is at least 2 and the Bass-Serre dimension of R is finite, then the quotient G(Φ, R)/E(Φ, R) is nilpotent by abelian. In particular, when G(Φ, R) is simply connected the quotient K _{1} (Φ, R) = G(Φ, R)/E(Φ, R) is nilpotent. This result was previously established by Bak for the series A1 and by Hazrat for C _{1} and D _{1} . As in the above papers we use the localisation-completion method of Bak, with some technical simplifications.

Original language | English |
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Pages (from-to) | 99-116 |

Number of pages | 18 |

Journal | Journal of Pure and Applied Algebra |

Volume | 179 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 1 Apr 2003 |

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