Resumen de Abstract simplicity of complete Kac-Moody groups over finite fields

Lisa Carbone, Mikhail Ershov, Gordon Ritter

• Let G be a Kac�Moody group over a finite field corresponding to a generalized Cartan matrix A, as constructed by Tits. It is known that G admits the structure of a BN-pair, and acts on its corresponding building. We study the complete Kac�Moody group which is defined to be the closure of G in the automorphism group of its building. Our main goal is to determine when complete Kac�Moody groups are abstractly simple, that is have no proper non-trivial normal subgroups. Abstract simplicity of was previously known to hold when A is of affine type. We extend this result to many indefinite cases, including all hyperbolic generalized Cartan matrices A of rank at least four. Our proof uses Tits� simplicity theorem for groups with a BN-pair and methods from the theory of pro-p groups.