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

Abstract

In \cite{CM06} Caprace and M\"uhlherr 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.