Uncountably many $2$-spherical groups of Kac-Moody type of rank $3$ over $\mathbb{F}_2$

Abstract

In this paper we show that Weyl-invariant commutator blueprints of type $(4, 4, 4)$ are faithful. As a consequence we answer a question of Tits from the late $1980$s about twin buildings. Moreover, we obtain the first example of a $2$-spherical Kac-Moody group over a finite field which is not finitely presented.