Simple groups of finite morley rank and Tits buildings

Linus Kramer, Katrin Tent, Hendrik Van Maldeghem
1999 Israel Journal of Mathematics  
THEOREM A: If ~3 is an infinite Moufang polygon of finite Morley rank, then ~3 is either the projective plane, the symplectic quadrangle, or the split Cayley hexagon over some algebraically closed field. In particular, ~3 is an algebraic polygon. It follows that any infinite simple group of finite Morley rank with a spherical Moufang BN-pair of Tits rank 2 is either PSL3(K), PSp4(K ) or G2(K) for some algebraically closed field K. Spherical irreducible buildings of Tits rank _> 3 are uniquely
more » ... termined by their rank 2 residues (i.e. polygons). Using Theorem A we show THEOREM B: If G is an infinite simple group of finite Morley rank with a spherical Moufang BN-pair of Tits rank ~ 2, then G is (interpretably) isomorphic to a simple algebraic group over an algebraically closed field.
doi:10.1007/bf02775036 fatcat:sum5rojxm5hrjdyrvmfm5uzzeu