BN-pairs of finite Morley rank where $B$ is solvable

Abstract

Let $G$ be a simple group of finite Morley rank with a definable irreducible BN-pair of (Tits) rank $2$ where $B$ is solvable and let $\fP$ be the associated generalized $n$-gon. If $n$ is odd and $B$ connected, then $n=3$ and $G$ is definably isomorphic to $PSL_3(K)$ for some algebraically closed field $K$. Furthermore, $n\leq 14$ if $T=B\cap N\neq 1$. We also give sufficient conditions for $G$ to be a simple algebraic group.