Bounded presentations of Kac–Moody groups

Abstract

Abstract. In this article we extend the result of Guralnick, Kantor, Kassabov and Lubotzky to the affine Kac–Moody groups: we show that there exists a constant such that every affine Kac–Moody group defined over a finite field , (with the exception of and ), has a presentation σ with . We then derive the consequences of this result for the 2-spherical Kac–Moody groups.