Isomorphisms of Groups of Kac-Moody Type Over ${\mathbb{F}}_2$

Abstract

In \cite{CM06} Caprace and Mühlherr solved the isomorphism problem for Kac-Moody groups of non-spherical type over finite fields of cardinality at least $4$. In this paper we solve the isomorphism problem for RGD-systems (e.g.\ Kac-Moody groups) over ${\mathbb{F}}_2$ whose type is $2$-complete and ${\tilde{A}}_2$-free.