### Abstract

Original language | English |
---|---|

Pages (from-to) | 99-116 |

Number of pages | 18 |

Journal | Journal of Pure and Applied Algebra |

Volume | 179(1-2) |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 01 Apr 2003 |

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*Journal of Pure and Applied Algebra*,

*179(1-2)*(1-2), 99-116. https://doi.org/10.1016/S0022-4049(02)00292-X

}

*Journal of Pure and Applied Algebra*, vol. 179(1-2), no. 1-2, pp. 99-116. https://doi.org/10.1016/S0022-4049(02)00292-X

**K1 of Chevalley groups are nilpotent.** / Hazrat, Roozbeh; Vavilov, N.

Research output: Contribution to journal › Article

TY - JOUR

T1 - K1 of Chevalley groups are nilpotent

AU - Hazrat, Roozbeh

AU - Vavilov, N.

PY - 2003/4/1

Y1 - 2003/4/1

N2 - Abstract Let F be a reduced irreducible root system and R be a commutative ring. Further, let G(F,R) be a Chevalley group of type F over R and E(F,R) be its elementary subgroup. We prove that if the rank of F is at least 2 and the Bass-Serre dimension of R is finite, then the quotient G(F,R)/E(F,R) is nilpotent by abelian. In particular, when G(F,R) is simply connected the quotient K1(F,R)=G(F,R)/E(F,R) is nilpotent. This result was previously established by Bak for the series A1 and by Hazrat for C1 and D1. As in the above papers we use the localisation-completion method of Bak, with some technical simplifications.

AB - Abstract Let F be a reduced irreducible root system and R be a commutative ring. Further, let G(F,R) be a Chevalley group of type F over R and E(F,R) be its elementary subgroup. We prove that if the rank of F is at least 2 and the Bass-Serre dimension of R is finite, then the quotient G(F,R)/E(F,R) is nilpotent by abelian. In particular, when G(F,R) is simply connected the quotient K1(F,R)=G(F,R)/E(F,R) is nilpotent. This result was previously established by Bak for the series A1 and by Hazrat for C1 and D1. As in the above papers we use the localisation-completion method of Bak, with some technical simplifications.

UR - http://www.scopus.com/inward/record.url?scp=0037398185&partnerID=8YFLogxK

U2 - 10.1016/S0022-4049(02)00292-X

DO - 10.1016/S0022-4049(02)00292-X

M3 - Article

VL - 179(1-2)

SP - 99

EP - 116

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 1-2

ER -