Finiteness Properties of Chevalley Groups over a Polynomial Ring over a Finite Field

2009/08/31 by Kai‐Uwe Bux, Bux, Kai-Uwe, Köhl, Ralf +2 · 1 citation
Computer Science · Mathematics · #20E42 #20F65 #20G30 #Advanced Algebra and Geometry #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.0908.4531

openalex publication_date 2009/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known from work by H. Abels and P. Abramenko that for a classical Fq-group G of rank n the arithemetic lattice G(Fq[t]) of Fq[t]-rational points is of type Fn-1 provided that q is large enough. We show that the statement is true without any assumption on q and for any isotropic, absolutely almost simple group G defined over Fq.

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