On groups of finite Morley rank with a split BN-pair of rank 1

Josh Wiscons
2011 Journal of Algebra  
We study groups of finite Morley rank with a split BN-pair of Tits rank 1 in the case where the normal complement to B ∩ N in B is infinite and abelian. For such groups, we give conditions ensuring that the standard action of G on the cosets of B is isomorphic to the natural action of PSL 2 (F ) on P 1 (F ) for F an algebraically closed field. In particular, we show that SL 2 (F ) and PSL 2 (F ) are the only infinite quasisimple L * -groups of finite Morley rank possessing a split BN-pair of
more » ... s rank 1 where the normal complement to B ∩ N in B is infinite abelian. Our approach is through the theory of Moufang sets and is tied to work attempting to classify the abelian Moufang sets of finite Morley rank.
doi:10.1016/j.jalgebra.2010.12.020 fatcat:glxlvvnd3jdotdmlvjc6o4kcn4