Finiteness Properties of Chevalley Groups over the Laurent Polynomial\n Ring over a Finite Field

2010/07/29 by Stefan Witzel, Witzel, Stefan
Computer Science · Mathematics · #20E42 #20F65 #51E42 #57M07 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1007.5216

openalex publication_date 2010/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if G is a Chevalley group of rank n and F_q[t,t^-1] is the\nring of Laurent polynomials over a finite field, then G(F_q[t,t^-1]) is of\ntype F_2n-1. This bound is optimal because it is known -- and we show again\n-- that the group is not of type F_2n.\n

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