On the non-amenability of the reflective quotient |
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Authors: | Chen Meiri |
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Institution: | 1.Department of Mathematics,Technion—Israel Institute of Technology,Haifa,Israel |
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Abstract: | Let O(f, ?) be the integral orthogonal group of an integral quadratic form f of signature (n, 1). Let R(f, ?) be the subgroup of O(f, ?) generated by all hyperbolic reflections. Vinberg Vi3] proved that if n ≥ 30 then the reflective quotient O(f, ?)/R(f, ?) is infinite. In this note we generalize Vinberg’s theorem and prove that if n ≥ 92 then O(f, ?)/R(f, ?) contains a non-abelian free group (and thus it is not amenable). |
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