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On groups of finite Morley rank with a split BN-pair of rank 1
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
doi:10.1016/j.jalgebra.2010.12.020
fatcat:glxlvvnd3jdotdmlvjc6o4kcn4