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

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

2010-07-29

arxiv.org/abs/1007.5216v1

Mathematics

Group Theory

36 pages, 4 figures

Scientific paper

We show that if G is a Chevalley group of rank n and F_q[t,t^{-1}] is the
ring of Laurent polynomials over a finite field, then G(F_q[t,t^{-1}]) is of
type F_{2n-1}. This bound is optimal because it is known -- and we show again
-- that the group is not of type F_{2n}.

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